Personally, I'm pretty sentimental about my bike (also a beater, but single speed) and want to keep it going almost no matter what. I think only the frame has remained the same throughout, and at times, I've definitely spent more than the bike is worth to fix it up.

I know that with cars, there's a definite cliff edge where it becomes prohibitively expensive to maintain compared to a new one. But I feel like that's not really true with bikes, perhaps because there are just fewer parts to replace, and it's less invasive to strip out any given part?

I suppose it depends on a few things. Do you have any sentimental attachments to it, and is there anything you would change about the bike if you were buying a new one? Do you think you can get a better one for $200?