The problem's not likely to resolve itself without some maintenance. F bodies are very reliable, but this is one problem I've encountered with at least a few so far. The faster shutter speeds become inconsistent or fail to expose the film, or the slow speeds become unreliable. The lubricants in the shutter will degrade over time or from lack of use, causing shutter capping or inconsistent speeds.
Since most F bodies are at least 50-60 years old, having to service the shutter is not unexpected, as it will be with all cameras. I suspect more than a few F bodies in use out there have never been serviced since they left the factory - which shows how reliable they are.
Just have a standard CLA done and you're likely to get 25+ years of solid use out of it.