That's odd. I know that laptops will suffer that problem sometimes, but my PC hasnt died in over 2 years and i leave it off for a week sometimes. I even once had a computer unplugged and boxed for two years and when it was plugged in i hit the switch and it made a weird starting noise and stopped, then hit again and it booted up fine. YMMV
Two of my old laptops with dead main batteries running Linux have the same problem.
I still turn off the surge protector on those since I use them mostly only seasonally (in winter) and put a new battery in them then.
On boot it returns the usual time error when dead but one can just click through and ignore the time.
A third laptop running win 10 has a good main battery which seems to keep the CMOS battery ok.
I use it maybe weekly and turn off the power bar/surge protector when not in use.
It can be hard to notice since windows went to auto time synch with the net and one may not get a warning about it.
Even more odd is when I boot Linux on my win10 machine even with a dead CMOS battery, It will maintain proper time once set even across reboots and days right up until I boot windows again and time goes out.
If I boot Linux after that, the time is out until I reset it and then it is ok until I boot windows again.
It is not a super common problem but others experience the same thing judging by Linux forum posts and other posts on other forums.
It is not affecting everyone on every machine.
If it was only my WIN10 PC, I would concede that it is just me.
I would prefer to turn the power off fully but it is a pain to change the battery at 3 month intervals.
I am no IT pro and have only built around 20 machines since I touched my first one in the seventies.
Regardless, I just wanted the OP to know the (possible) risks of turning off the surge protector.
Your particular results may vary.