One of the best ways this ends is you get acquired by your competitor. Either you make a quick buck and start the next one, or you have a nice comfy job with great pay.
You could also try the Netflix route of "become HBO before HBO becomes Netflix" if you can copy all of your competitors features at a lower cost, better quality, etc.
You could not classify as a startup but instead just be a small business and slow your growth. That way you get a steady income for your own company, but not get big enough to threaten your competition.
Or you could figure out what other related needs your niche has that are unmet and differentiate yourself that way. That way you build a name for yourself in that niche and it's more than one feature that needs to be copied. Take your feature and turn it into a full product. Focus on your niche, not the broad audience your competitors have. What do your customers need that the big guys aren't doing? You're a startup, move fast and break things.
Just a few options. The worst option (IMO) is to keep your product just a feature until finally your lunch is eaten and you're out of business. I've had that happen. Doesn't feel good. Innovate, that's why you're a startup.