@scylla and @kabayan covered the essential basics.
Generally I am reluctant to comment on the probability of making a successful H&C case. There are many variables. There is almost no limit on what factors can be considered. How this or that factor influences things can vary a lot, including the same factor having a virtually opposite influence for one individual compared to another, depending on context and how that factor relates to other factors. It can get complicated. Forecasting outcomes is extremely difficult.
Generally, to the extent the PR can explain why he or she remained abroad, that is what the PR relying on H&C reasons should do: give IRCC, or once the matter is on appeal give the IAD, a complete explanation for all the reasons the PR has been abroad. This includes explanations many in this forum will say do not count. Like remaining abroad for employment or business reasons. A full and truthful explanation covering how and why the PR did not come to Canada to settle sooner and how and why the PR remained abroad otherwise, including some accounting of efforts to get to Canada to stay, is generally the best the PR can do, and hope his or her explanation persuades IRCC, or the IAD in an appeal, to allow the PR to keep PR status
DESPITE failing to comply with the Residency Obligation.
The PR RO H&C case is very different from other H&C cases. Yes, like other H&C cases, compelling humane and compassionate circumstances will make the case. A PR who was kidnapped and held hostage for years abroad is not going to be denied H&C relief. BUT for PRs the nature and scope of H&C relief can and often does go well beyond the parameters of what are considered compelling H&C factors in other cases. IRCC, and the IAD, will consider and oft times make favourable decisions based on factors which are more about whether the PR, in effect,
DESERVES a chance to keep PR status, a chance to settle and live PERMANENTLY in Canada.
This makes it very, very difficult to predict the outcome of the PR RO H&C case. Statistical odds are LOW absent typical compelling H&C factors, but the outcome is not based on statistical odds. The outcome is not determined by the spin of a roulette wheel or other game of chance. The outcome depends on the individual, the specific facts and circumstances and deserts (what the PR deserves) for the particular PR who often is, in effect, basically asking for a chance to settle and live in Canada despite failing to meet the RO.
Thus, I am reluctant to comment on the probability of making a successful H&C case because how it is likely to go depends on way, way too many factors that are very difficult to assess. Absent typically compelling H&C reasons (the individual faces torture if deported; or the individual is the only parent who can care for minor children who are Canadians and who know no other life than a life in Canada; or such), the odds are NOT good but various circumstances can persuade Canada to allow the PR to keep status and a chance to live in Canada permanently . . . the latter depending a lot on how big the breach was.
That said,
many H&C cases are NOT a close call.
For many cases there is little or no reason to entertain false hope, or to spend a lot of money and effort pursuing an appeal. And that appears to be the crux of the query here, whether the OP has a case worth investing money, effort, and time to pursue the chance of a favourable IAD decision allowing the OP to retain PR status based on H&C reasons.
As I noted, again (it warrants emphasis), generally I am reluctant to comment on the probability of making a successful H&C case. Whether to proceed is very much a personal decision. For example, what the individual can afford is a big factor in deciding whether to spend the money for a lawyer, totally apart and separate from the merits of the H&C case itself. Among other factors apart from the merits (the strength) of the H&C case itself, one is the prospect of obtaining PR status anew as suggested by
@scylla.
Of course the strength of the H&C case is the key factor in making the personal decision about whether to appeal and whether to spend the money for a lawyer in prosecuting the appeal.
Note: you can appeal and make the case yourself, as best you can, without a lawyer. Odds of successfully doing so are probably not good, but the only downside is if you have an alternative plan to reapply for PR, you cannot do that until there is a final decision on the appeal or you withdraw the appeal. If you do this, if you pursue an appeal, give the IAD a complete explanation for ANY and ALL reasons for remaining and going abroad. Just lay your entire situation out for the IAD to consider. Thus, while a lawyer can probably BETTER put together the case to make to the IAD, you can do it yourself, and if you do, then be sure to explain the whole story, truthfully, and then all you can do is hope for the best.
Also note: There is usually some possibility IRCC (the Visa Office) failed to follow the law and proper procedure, which would be grounds for the IAD to set aside the decision denying the application for a PR Travel Document. This is a more difficult case to make and even with a very good lawyer the odds of success, on this ground, are NOT at all good. That is, the odds are very high that the decision was valid in law and will be upheld in this regard (given your acknowledgement that you were well short of complying with the RO).
That is, you have been determined to be in breach of the PR Residency Obligation and it is highly likely this determination is valid in law.
That leaves you with the H&C case.
Some further observations regarding the strength of the H&C case:
As noted, there are many factors which may be considered in evaluating whether there are H&C reasons for allowing a PR to keep PR status despite breaching the RO.
The reasons why the PR remained abroad are a big factor of course. But the nature and extent of the PR's connection to Canada, and especially the PR's ties to living a life IN Canada, are also huge factors. Overall, nonetheless, how many days the PR has been in Canada is the biggest factor.
HOWEVER, there is one factor which looms rather large in the factual circumstances described here: it appears you were
ALREADY in
BREACH of the PR Residency Obligation
BEFORE you left Canada due to your parent's death.
For purposes of calculating whether there was a breach of the RO, only the five year period of time prior to the date you made the PR TD application is considered. Since you spent more than a year in Canada, it is not a totally egregious breach, but it is not like you were close. 1400 days abroad compared to 400 in Canada, some ten months or so short of the bare minimum, there is no doubt about you substantially breaching the RO.
For purposes of assessing H&C factors, the PR's overall history and connections to Canada and time in Canada, can be and likely will be considered. And again, based on what you describe, it appears
you were already in BREACH BEFORE you left Canada due to your parent's death. Moreover, your personal ties REMAIN largely outside Canada. Where your family has been living these past years is relevant. The fact they have not been living in Canada further shows your primary ties are OUTSIDE Canada, NOT in Canada.
I remain reluctant to so much as suggest how you should proceed. But in terms of what you have shared in this forum (including other topics and other parts of the forum), there is not much to indicate you can make a persuasive case even if you have the assistance of the best lawyers.
For clarity: There is no process for renewing PR. Not individually. Not for a family.
I get it, that it is likely this comment was not really about "renewing PR." But it needs to be clear, there is NO need to renew PR. There is NO process or procedure for renewing PR.