As I have a 2007 as well, I wish could provide the answer, but the symptoms, as described, are not something I've experienced, or read about here or on other Subaru forums, and they don't fit any of my understanding of the keyless entry/security system.
But there might be something relevant in other observations that we don't yet have. For example, when the car is turned off and the key removed, does the security light in the instrument panel flash as it should? Does it go out when the key is inserted?
Does the remote lock and unlock function work? (Locks and unlocks the doors, external lights flash, and there's an audible signal at the same time.)
Do any of the warning lights in the instrument panel stay on after the engine is started?
Are there any other electrical functions that are not working properly?
Is the battery in good condition and properly charged up? Is the electrical wiring at the battery, and at the ground wires to the body and the engine in good condition?
Is the car new to your grandfather, or was it bought some time ago and keyless entry/security didn't do this for [how long?]. The problem only appeared [when?]. If the problem only recently appeared, what work, if any, was done on the car before the symptoms appeared?
Admittedly it's a gunshot approach to see if anything else might provide a lead.
In the event the car is taken to a garage and the problem is identified and corrected, I hope you will let us know what it was.