Trying to log into admin area https://thelabelmachine.com/forums/admin

See more detail here https://www.loom.com/share/88a6941973b14080beae862153ed26ac

I recently moved to the new subscription model - could it be related to that? 

Please contact your hosting provider for assistance here. Typically, 502/503 have a server related issue. 
 

You may also wish to try recovery mode if you’re using third party addons.