Does Construct 2 have the issue where you have to connect to the internet every 7 days to verify? I can't use Construct 3 since I'm without internet 6-8 months out of the year on average.
No. Construct 2 is an offline application, so you don't have to update or re-login every 7 days unlike Construct 3.
The benefit of Construct 3's online subscription is that you have constant update and support for new features, bug fixes, 3rd party compatibility, technology updates and etc. This is very essential for developers who commercialize their games.
If you don't have internet for that long period of time and maybe constantly travel and/or are on remote places. Then, I assume you don't make commercial games and do this mainly as a hobby. Then, I do think and recommend you go with Construct 2.
I remind you though that Construct 2 is 1.6x more expensive than it was before. And also, it is outdated and Construct 3 was made to replace Construct 2.
Construct 3 :: $99.00 per year.
Construct 2 Before :: $120.00. One-time payment.
Construct 2 Now :: $199.00. One-time payment.