OVERALL OBSERVATION WORTH EMPHASIS: Canadian Permanent Residents SHOULD keep a detailed, complete, up-to-date log of ALL trips abroad. Including day-trips to the U.S.
Beyond that . . .
This question deserves emphatic attention in this context. The OP's query is not at all clear about what kind of application is being made.
Giving a definite answer (such as some have given) to uncertain questions risks getting it way wrong.
That said, without trying to review every possible kind of PR-related application there is, at least MOST if not ALL questions asking for detailed dates of travel outside Canada ASK for details including DAY-TRIPS to the U.S. Including applications for grant citizenship.
So the safer, if not entirely correct response to the question about whether to include day trips to the U.S., is YES. At least for most if not all PR related applications.
A couple of the responses above are clearly addressing the question in the context of an application to renew a PR card. And that is indeed one of the applications for which a PR is asked to provide detailed travel history, Item 21 in the 02-2019 version of the application (which I think is still the current version used), in which the instruction to detail ALL trips outside Canada is clear.
Day-trips do not affect the total calculation of days present IN Canada. Even an overnight trip does not affect the calculation (since day of exit and day of entry both count as a day IN Canada, since at least part of the day was indeed IN Canada, and this is true for grant citizenship applications as well).
The OP's question appears to be about something else. But since this forum is about PR Obligations, the responses based on what information needs to be included in a PR card application (in contrast to an application for a PR visa or for PR status) are appropriate here. Regarding which, again, as others say, YES, the PR should report ALL trips including day trips to the U.S.
How the failure to disclose day-trips might affect a given PR card renewal application, HOWEVER, can vary widely. Even more so for grant citizenship applications.
Leading to . . .
Well, let's be clear, there is a definite obligation to report day trips. Just "
for the heck of it" is OK if it is actually done. But failing to properly report all international travel, even day trips,
RISKS problems.
In terms of failing to properly report all trips, like many aspects of immigration related procedures, the fact that one or many
GET-AWAY-WITH-IT is
NOT at all a good model to follow. BUT of course, how it actually goes depends a great deal on the particular individual's circumstances.
Take the circumstances described by
@DC1018 . . . the irony is that many day-trips, for many PRs, will tend to indicate a pattern that more or less reinforces an overall showing of a life IN Canada. IRCC can and will if needed verify dates of entry in the PR's CBSA travel history. IRCC can also access road trip entry into the U.S. information directly from U.S. records (unless the PR is a U.S. citizen, and even this is changing). So it is relatively easy for IRCC to examine such records and affirm that, at the least, the PR has an ongoing residence in Canada.
In contrast, the PR with far fewer trips to the U.S. may actually end up under more scrutiny in the process to verify the PR's travel history, if the PR fails to report one or more of those trips. More so for a grant citizenship application, given both the higher minimum threshold for meeting the requirement and the weight of what is at stake (granting citizenship is a very big deal; in contrast, issuing a new PR card does NOT have much effect on a PR's status, since even the day after the PR receives a new PR card, the PR can face a Residency Obligation examination and if not in compliance, issued a Departure Order).
With a small number of trips, there may be no readily discernible pattern.
Numerous trips tend to illuminate a pattern. And for a PR who is actually living in Canada, a pattern indicating this will likely be readily apparent.
It warrants noting, for example, that many grant citizenship applicants are surprised by RQ-related requests when they report very few trips abroad. Overlooking the tendency of many trips to show a pattern which can, and often will, reinforce their reported life IN Canada.
Thus, for example, in the grant citizenship application process (there are more reported cases regarding presence-in-Canada calculations for citizenship than PR card renewal, since for the latter, in close cases IRCC does not overtly engage in a formal RO compliance examination but, instead, tends to refer the application to Secondary Review and then sees where the PR is at six months or a year later), there can be very stark contrasts in who gets RQ'd. We have seen credible reports of applicants RQ'd apparently because they failed to report a SINGLE day trip, just one trip not reported, BUT IN CONTRAST other credible reports of NO RQ related requests or any other non-routine processing DESPITE the applicant failing (overlooking) a trip abroad for THREE WEEKS.
Lots of various factors can influence how it goes. The margin over the requirement can have a big influence in whether or not an IRCC official has concerns, and in particular, as
@DC1018 alludes, if omitting travel dates affects the calculation to the extent it means the PR falls short, that can make a big, big difference -- for PR card renewals, falling short by a little probably does not result in a negative outcome unless the PR has, in the meantime, gone abroad; but for grant citizenship applications, falling short by just one day will necessarily result in ineligibility and the application being denied.
THE MAIN TAKE-AWAY: The point is that PR's should keep a detailed record of ALL international travel, including day-trips to the U.S., and make a concerted effort to ACCURATELY report ALL trips when applying for a new PR card, for a PR Travel Document, or for citizenship.
Even though the failure to do this may not have a serious detrimental impact for some PRs, how a failure to provide complete, accurate information, including all day trips, can vary widely and can range from minimal impact to serious non-routine processing and related delays, or in some cases, a negative outcome (more so for citizenship applications than PR card renewals, again as long as the PR is actually living in Canada).
AND it is important to be aware of the CREDIBILITY factor. The failure to be an accurate reporter may not have direct, negative impact, but it can influence how decision-makers approach the PR and the PR's other information. Never good to be a more or less obvious unreliable reporter of facts. Second only to meeting actual requirements and following the instructions, the PR's credibility is often the next most important factor in any application or immigration related proceeding.