There has to be a filter on the fuel pump, I would look there, but yes, there likely isn't another filter.
I had an issue with my old honda car, it would only go upto 50mph, if you babied it, hit the gas hard and it would stall. The checkvalve in the fuel line feeding the engine was bad, and was restricting flow, so it couldn't meet the high demand when I needed to burn more gas.
Once I finally located and replaced that checkvalve is when my real issues started though. I found out I had 0% clutch live left, but since I had always had to baby it, I never knew.
From what you said, it works for a few min, then starts to die. Sounds like it cannot suck in gas fast enough to the fuel pump, so once you use up what you have in the line, it starts to sputter, give it a chance to catch up, and it's ok again for alittle bit. I would make sure all the hoses and filter and check the fuel pump itself if there is something in it's internal hoses or filters. After that I personally would likely change the fuel pump (after making sure I didn't overlook any other cheaper solutions).