Or choose free software. If it's free software, even if the original developer goes away, you can hire someone to keep working on it, or someone else can decide to make a business supporting it, or the like.
Or you just get left with a broken OSS project whose contributors moved on to shinier things, and nobody really much cares about continuing it, and you don't have the knowledge/time/resources to hire someone to do it.
But if the product is already working, chances are that you get away long enough (to do a graceful migration) by just doing small bug fixes, changes to support OS updates, etc.
This is what we are now doing for a project with Berkeley DB XML, which hadn't seen updates for five years. When there finally was an update, it was buggy and moved to the Affero GPL 3, which conflicts with other open source licenses used in the project. So, we continue to use the five year old iteration with a small set of patches.
(Lesson learned: once a product is owned by Oracle, prepare your evacuation plans.)
I was agreeing with the previous posters until I realized this has kind of happened to me. Tastypie was the go-to REST package for Django 3 years ago. Now it has kind of been abandoned and everyone is ranting about Django-REST-Framework.
Fortunately it is stable (for my use cases), and it doesn't actually seem ton be that big a deal that it isn't being worked on. Django_REST_framework is a lot nicer though.
One of the problems you get is that once something is stable, the maintainers generally don't have a huge incentive to dedicate already-over-committed time to work on features they don't personally need. Just triaging tickets on a popular project can be a major time commitment, particularly since a fair percentage of them will be helping people understand the API or trouble-shoot something in their project which is causing failures in your code.
In the case of tastypie, I think all of the maintainers have switched jobs at least once in the last few years and at the same time the general Django community has been moving in the direction of simplicity rather than complex generic frameworks. Daniel's list of things he's not interested in implementing in restless is a good list of things which have been painful in tastypie: https://github.com/toastdriven/restless#anti-features
Like I say, it is stable for what I am using it for just now.
I have started using REST framework for other parts of the project, and it seems a lot more consistent with Django's other components (serializers are similar to forms, APIViews are similar to the generic views). In the end that just makes things easier. Its less context switching essentially, which is really useful when I don't touch that part of the project for a few months, then need to update something.
Thanks for the offer though (and thanks for the framework, it has been useful). And unfortunately I don't have the time to help with maintenance.