Battery problem cal. 1365

It really needs to go to a watchmaker who can diagnose the problem. Could be excessive drag caused by debris in the movement train, could be a short circuit caused by old electrolyte etc etc.

What batteries are you using?

That is a pre-Swatch Omega. It has to be close to 50 years old. Parts if required, may or may not be a problem. If there is a problem with the watch that is actually killing cells, I am surprised that it runs at all. You may not have any choice but to shell out and have it serviced.

Your chances of finding a movement are probably slim. And if you were to find one, it may not be in as good shape as the one you have. Put a little more effort in trying to remedy the one you have.

I have a number of threads on the 134x movement calibers.
I looked up 1365. This has a linear motor rather than the round stepper.

As others said, find a good watchmaker. Although these early movements are a special skill. The movements in these are mechanical with metal plates. So those parts need traditional cleaning.

The electronics on the other hand can be tricky. As noted the chip foundries long since turned to dust, and the designs shredded. Back then chips were hand draw on film. No computers to do the layout. Even how to do it is no longer known.

This time is referred to as the 'quartz' crisis. There was a lot of experimentation happening. Some variations were produced in large quantity. Others not so. Eventually it was found to make the movements plastic, and disposable. Took until the mid 1990s for things to settle down after the consolidation of the industry.

Outside omega, the only source of parts is the second hand market. Old maker estates and such. Often the sellers do not know what they have. Those who do work with this type of watch keep a close eye on auction listings and old material house stock. So there is a bit of competition.