Other than the initial idea of going to the vet to check for UTI which I think might be a good idea, have you tried limit his water consumption to certain times?

My little guys initial problem was that we let him have free access to water whenever he wanted. He would drink every now and then causing his pee times to be very irregular. When we started restricting it he definitely seemed to have more control. Especially since we would try to time giving him a bunch of water right before going for a walk.

I'll illustrate this a bit further . . .

7:45 we wake and take him out, he pees and praise/treat party 8:00am he drinks water 8:15 he drinks a little more 8:45 he drinks a little more 9:00 we take him out and he pees, praise and party Now here you would think that he can hold it another hour(Til 10:00) at least but nooooo this is where I think we made our mistake. It's 9:15 now and his bladder has just processed the water from 8:15 or 8:45 and he has to pee again, he cant hold it because the pressure is getting really intense so he goes inside and now we have an accident.

When we switched to this schedule his accidents drastically disappeared.

7:45 wake up, take him out 8:00 free access to as much water as he wants. 8:05 water goes away. 9:00 take him out again. 10:00 Water access again, 5 mins 11:00 take him out . . . ECT

Maybe you could try this and it might help. Keep in mind I have absolutely no idea about how fast puppies process water, this is just what worked for me. Additionally I am by no means saying to limit your puppies water so much that he isn't getting enough daily. Definitely be sure he is drinking atleast the recommended amount. Also we slowly introduced him back to having full access to water all the time as he got better at holding it. He's almost 6 months now and hasn't had an accident in well over 2 months.

Oh, Also set a timer on phone so you can be exactly sure that you are taking him out at whatever time you decide. That way you can know when you are making progress and can try moving up the time.

Anyways . . . Good luck!