Can I retry the "Broken rental car" random encounter?

This handsome devil?

There are some that call him... ..Timm.

Apparently, this random event is one of the repeatable ones - even after successfully finishing it:

I'd like to confirm out loud that the slick business man who needs a ride to the airport and tells you to invest in Tinkle because he's about to wow a boardroom [?] totally [screws] his car up more than once.

I gave him a ride as Franklin sometime right before the last mission and invested heavily with all three characters, riding the stock up 30%. After the last mission, I ran into him again as Michael, in a totally different time and place, and invested even heavier.

As an extra tip, you'd best invest as much as you can into Tinkle stock beforehand, so you can sell them with a 33% profit after this event:

Before pursuing this Random Event, take the time to switch to all three characters first and invest all your money in Tinkle (TNK) on the BAWSAQ page. Once that's done, activate the Random Event with Trevor.
^source