The real issue with Rails apps is keeping up with the framework and language versions. There are really two categories of dependencies.
One-off libraries that don't have a runtime dependency on Rails are typically very low-maintenance. You can mostly leave them alone (even a security vulnerability is unlikely to be exploitable for how you're using one of these, as often user input isn't even getting through to them). For instance a gem you install to communicate with the stripe API is not typically going to break when you upgrade Rails. Or adding httparty to make some API requests to other services.
Then there are libraries that are really framework extensions, like devise for authentication or rspec for testing. These are tightly coupled to Rails, sometimes to its private internals, and you get all sorts of nasty compatibility issues when the framework changes. You have to upgrade Rails itself because you really do need to care about security support at that level, even for a relatively small company, so you can end up in a situation where leaving these other dependencies to fester makes upgrading Rails very hard.
(I run a startup that's a software-enabled service to upgrade old Rails apps).