Westec 5000, after all these years is acting up

I'll try to describe the problem.

We have an elaborate (25 zones all hardwired) burglar alarm system, a Westec 5000 from probably the early 1990s.  ADT is our monitoring company and used to be the servicing company but they no longer service hardwired systems.

The alarm system has been working perfectly for over two decades until a few days ago when one door, which is never opened, started to trigger the alarm as though the door were open.  This occurs as often as once ever 7 hours to a couple times an hour; in other words, it's very irregular.  

Since this happened, the work-around  we use is to simply "bypass" this door (zone) when we set the alarm, i.e., when we arm the system.

A few days after the problem started, I replaced the switch on the door (a Sentrol 1075/65 about an 1.25" long) with a new one (a PS-1650 about 5/8" long) but the problem is still occurring.

Because of this, I then tested the old switch with an ohm meter and it seems to be a functional switch.

Also, even with the new switch if I open the door according to the LCD Display (the keypad) the door is closed; if left open, sometimes, say for another 10 minutes it may finally show as being open on the LCD Display.  

On the thought that the problem may be in the control board (God was a mess of wires!), I spliced together the two wires just before they reach this door's switch (the one I just replaced); the intent is to "take the door out of the system" such that if the LCD Display now ever shows that the door is open (even though it is now hardwired closed) the problem would point to the control board.
 
For such a localized problem in a system that otherwise satisfies all of our home security needs...we don't want to "upgrade" to a new wireless system.

Thoughts?
Ideas?

Thanks
 

If the problem is a bad zone input on the panel, you may be able to move the wires to a different, unused zone input, assuming there is one.
 
If there are no unused zone inputs, you could merge the door contact in with another zone. 
 
If the problem turns out to be bad wiring to the door contact, then it's "easier" to solve.  Just run new wiring (which may be a bit of pain).
 
If it were me, and it turns out that the panel has a problem, I'd bite the bullet and replace it with a new system.  You should be able to keep all your hard wired zones.  You'd just have to replace the panel board and keypads.   It'll be a bit of work to rewire, but that's something that's done all the time.   One thing that would make it a bigger pain is if the contacts are wired with EOL resistors and they are different values than the new system uses.
 
If ADT won't support hard wired systems, there are other monitoring companies out there. 

Since you know the zone, why not just bypass it at the panel either with a resistor or just a piece of wire?  If it happens again, then you know it is the panel.  If it doesn't, then you know it is the wiring.
 
It would seem to me that since it can take 10 minutes before it notices the door is open that the problem would be at the panel.  The wiring isn't doing much; just allow the circuit to either be open or closed via the sensor.

Thank you so much guys.  Excellent and very clear advice.  Big hug!