My girlfriend was issued a citation for driving while under suspension. A few months later, she was pulled over again just because the same officer recognized the vehicle. Anyone could have been driving that car, including me. Does that officer have the right to pull the vehicle over? Is that probable cause?

To be honest with you your girlfriend may be not telling you 100% story. An officer has nothing against your girlfriends car and would not pull over a car just because he recognized it.

No one will risk there job because of what you feel is "probable cause"

I will add, unless this is a small town of 5000 people, a officer will not remember a car from 3 months ago.

But if they did remember the car, and reconised the driver as someone that was suspended, that is a reason to stop them.

But reasons to stop.
As a officer in Georgia I used to laugh about 2 out of every 3 cars has a reason for a stop. Many have some novelty plate cover, like a team sport or a cause that is over the rear plate, well almost all of them slightly or move cover the county name, the state name or the year sticker.
All reasons. Many cars have some sticker in the back window. The officer can stop the car to check to be sure that the rear vision is not blocked.
Is there something hanging from the rear view mirror, illegal in most starts, GA for sure, reason to stop them.
And I could go on for pages of silly little known laws about cars that allowed me to stop them

More than likely more happened the second time it was pulled over. Police officers do not have time to pull someone over for no reason. Unless it was a possible suspicion of a vehicle used in a crime or the driver fit a certain description of a wanted suspect, there was more to it than that. In Florida, the probable cause has to almost be seen. For example, plain sight or smell, motor vehicle violations or speeding, lane changing etc...