I'd even be willing to pay the $99 a year, I just want the signature to last longer than a week, ideally forever. For years when I don't feel like updating the app, I won't pay the developer membership fee.
I think the deploy straight from Xcode to your device builds have a pretty short lifetime (I remember it being a month in around 2014 or 2015) not sure now.
If you archive and build using a certificate from developer.apple.com they last a year.
As someone with dozens of side loaded iOS apps, all of my apps are working just fine, well over 6 months later. I always build and deploy without archiving.
