Disagree w/Beta03.
There is indeed a maximum.
There are three factors that will determine the maximum score.
1. The time limit. GEx runs ONLY from Tuesday 'til Sunday. 24 hours it's true, but still a limited amount of time.
2. The size of your wallet.
a). For poor people (moi'). I will have but 24 * 6 tries at GEx map. Period.
b). For wealthy people (non moi') you can break out to plastic and buy diamonds and then spend
those diamonds on extra chances, but ONLY IN THE TIME LIMIT PROVIDED (ie: 6 *24 hours). And remember, YOU NEED TO FAIL to get that maximum count. This is what is known as 'Flushing Money Down the Crapper'.
3. For those lucky enough (non moi', encore), you can collect medals via PvP tower and/or incidents and/or Daily Challenges.
These medals can also be used to purchase additional bites at the GEx apple, but again, ONLY IN THE TIME LIMIT PROVIDED.
So, clearly, yes there is a maximum. You are limited only by the diamonds/medals you wish to spend.
I leave it to others more owning of Conditions 1/2/3 (or any combination thereof) to provide the answer.
Or, take the easy way and just participate few hours per day and keep track. Then you will know your maximum.
You're welcome.