Water stops running after 10 minutes...well or well pump?

I just had a home inspection on a home I've signed the contract on. I had to leave before the end of the inspection, but the inspector called me and said that he had the water running (the home has a well) to do a septic tank test and after about 10 minutes, it would only dribble water. He said he turned it off and waited a little bit and turned it back on and it worked fine for about 10 minutes and then dribbled again. Does this "sound" like a problem with the actual well or maybe just the well pump needs to be replaced? Obviously I'm getting an inspection by a well professional, but I've just been wondering. If it's the actual well, I think I've lost my interest unless the seller will fix it, which he probably won't.