Could a fighter aircraft be operated indefinitely?
Yes and no. In Cambridgeshire we still have some Spitfires and other Second World War aircraft which are still operated more than 60 years after being built. The Shuttleworth Collection even flies some First World War and pre-war aircraft. It's demonstrably possible to keep operating a military aircraft for at least a century after it's built.

But that's not useful if the aircraft has no military value. None of the examples I've mentioned are still operated as military aircraft: they're in civilian hands, performing for displays, mostly for their historic value (though many ex-military aircraft in civil use are performing other functions, such as air transport or crop spraying).

Aircraft get retired for two reasons. The most obvious is that they're superseded by newer types, newer designs with better technologies and materials. The first air force that tried to field one of these Spitfires in combat against modern jet fighters would quickly realise it had no military value whatsoever.

The second reason is that they get increasingly expensive to maintain. Military aircraft especially can be very fussy about fuels and parts. Maintenance might require special fabrication of small numbers of parts or tools, which gets more expensive when the rest of the industry has moved on. (For example, the Tiger Moths I fly have one particular part that's impossible to obtain, because the alloy it's made of isn't produced any more.)

For this reason, although there are still surviving, operating aircraft from the earliest days of military aviation, it wouldn't be feasible or useful to continue operating them as combat aircraft.