Sims can't reapply to university

@davyjoonslocker 
To help with your issue a few questions need to be asked.
Are all three Sims in the same household?
Did all three show with a completed degree?
As long as these two things apply to your Sims they all should be able to enter to earn another degree.

Do you have mods/custom content of any kind?
Just realized you already said you use mods.

Controlling your Sims to study, complete projects like term papers and presentations to get good grades is important to successfully complete a full degree. If the degree is not completed your Sim cannot enroll again. At least not for a bit.  To test look on the phone got the option to drop out of university.

Mods / cc can inadvertently change how the game works. Testing on a new game the best way to find out what happened and get the game back in working order. 
The simplest way is to do the following steps:
Rename your The Sims4 folder in Documents\ElectronicArts to The Sims4_Backup
That will preserve all your saves and content so nothing is lost.

Do not put anything back.
Test with a new save game to see if the issues are still there.
If the game works correctly you will need to test your mods /custom content (CC) to see which they are causing the problem.
When adding/testing/deleting mods and/or cc it is important to delete the localthumbcache.package and any other cache files.
Using the 50/50 method is suggested to speed up the process.

Additional instructions are in the link below:
Troubleshooting tips
https://answers.ea.com/t5/Technical-Issues-PC/READ-FIRST-Troubleshooting-your-Game/m-p/3621199

EQ Avid Sims Player
#EQCreations
I do not work for EA
All packs installed and patches are current.
PC / Win 10
Never used CC or mods.