I work as a cybersecurity research analyst/security architect for a U.S. company. My work is 99.9% remote. I own property in Nova Scotia - that I have just purchased as a "safe harbor". I plan on working for at least 5 more years - the work is physically non-demanding and I really enjoy it. I will also start collecting my social security pension next month.
Because of my age (66) - I have been told that it will be difficult for me to gain any kind of residency status. I'd like to know if that is true.
As a working professional, yes - it will be difficult, since you're one year away from retirement age. Regardless of your age, if you were able to find a Canadian employer willing to apply for an LMIA for you, that would be a path to later permanent residence. I haven't heard of LMIA/work permits being refused because of age...
Alternatives: People with lots of money can buy their way in as "investors." There is the family class option - have you looked at MapleMatch.com (or any of the dozen or so other dating websites)? LOL.
If it IS true, what are the restrictions about leaving and re-entering the country to "re-set" the 180 day clock cycle.
Umm... Not sure about this. Probably safest to think of it in similar terms (or the reverse) as Snowbirds. When Canadian snowbirds go to the USA, they are tolerated for up to 6 months (cumulative) without triggering any residency questions. You would need a different haven for the other 6 months.
http://www.cbc.ca/news/canada/canadian-snowbirds-rules-you-need-to-know-1.2925513
On the other hand - A few years back, I had a Canadian friend who would fly back to Canada once every 6 months for a week, so that she could stay with her student partner... took her two years to get a work permit to stay, but was never refused re-entry to the US. Rules are fairly well harmonized between the two countries, so you might try it, keeping in mind that things change, esp. with better electronic tracking.
RE your work - as long as none of your clients are Canadian, working remotely while "visiting" would not require a work permit.