I found a solution to my problem!
Over the last 8 years that I owned my 1998 Subaru Outback Limited Edition Wagon, a particular one of my keyless entry remotes failed three times. Up until the last year, I had the luxury of taking my Subaru back to the dealership where I purchased it and they would re-program the remote for free.
This last year, I since moved and had to take my Subaru to a new dealership where they like to charge for this kind of service, so I lived using only one of my keyless entry remotes. This turns out to be the problem. It appears that the alarm electronic control unit needs to have two keyless entry remotes programmed to it. If you leave it with only one single keyless remote programmed to it, it becomes sensitive to all other worldly remotes.
Solution to problem:
Re-Program BOTH keyless entry remotes to your Subaru! I have a Code Alarm System and it appears to be sensitive to other peoples remotes if you have only a single keyless entry remote programmed to it.