I just did some testing. I've been out of town so the car sat in the garage all weekend. I normally use keyfob #2 and keep #1 as a spare. I've replaced the battery in fob #2 twice.
I took fob #2 out to the garage. The driver's door didn't unlock when I placed my hand on the door handle. I tried it a few times with no luck. After pulling on the handle a few times it finally unlocked, as usual.
I went back into the house and grabbed fob #1. I left #2 in the house and took #1 out to the car.. It worked perfectly!
OK.. that told me it could be the battery in #2. I swapped batteries between the two fobs. Using the battery from #1, fob #2 worked perfectly with unlocking/locking the doors with a hand on the handle. I was even able to lock/unlock the car using the buttons from more than 20 yards away.
The real confirmation was if fob #1 didn't work using fob #2's battery. I took fob #1 out there (using fob #2's battery) and it worked fine. So much for the scientific approach.
I'm driving to lunch in a few minutes so I'll test fob #2 in normal driving situations.