I'd say it's mostly based on personal preference. If you don't use a framework, you will end up reinventing a lot of stuff that's in mainstream frameworks. OTOH, the stuff you spend reinventing really won't take you much longer than learning the framework, as long as you build off a decent set of libraries (don't try to reinvent your own templating-library/HTML-escaping/database-interface etc.) And if you do switch to a framework, you'll probably be better able to understand the reasoning behind why the framework did what it did.
One other consideration: frameworks make it much easier for somebody new to get up-to-speed with your code, and often tackle thorny deployment issues that you can spend a lot of time on otherwise. Keep that in mind when deciding - for a startup, the priority is to get something up on screen so you can see if you're on the right track, but you do eventually want to be able to grow and scale.