There are two generations of the 6305. One has a shaft that stays fixed inside the motorblock. The other has a removable shaft that has bushings on the end. I'm assuming here that you have the version with the removable shaft and bushings. If you have the fixed shaft version, ignore the instructions below and let me know. Also, if you've been running the 6305 on a controller, please disconnect it from that to help isolate the problem.
The most common cause of this is a propeller that doesn't spin freely on the shaft. Please remove the cover of the pump and slide out the entire propeller and drive unit together with the shaft. Inspect the blue bushings to make sure they are not torn or damaged in any way. The bushings keep the shaft centered, and if they are damaged or not fully seated, it can result in the intermittent stopping you described.
Next check that the propeller and magnet assembly can spin on the shaft with (almost) no resistance. Any calcification on the shaft or inside the magnet will cause friction which the pump will sense. When it senses that friction it shuts down to prevent damage. So make sure it spins freely. Also make sure the shaft isn't bent at all and that there aren't any nicks or wear marks anywhere in the propeller or magnet.
It could also be a power supply problem. If you have another 6305 with a working power supply, try swapping the power supplies to see if the problem stays with the same pump or if it follows the power supply.
If all of the above seem to be fine, then the next step will be to send it in to us for a closer inspection. Let me know how this goes and we'll take it from there...