Custom AE deadlocking after PUM 25

I have one custom app engine that has been in production for weeks is now failing after PUM 25 installation. However, I cannot recreate the error on any of my test environments, even with the PUM update. This app engine is failing only on production, and I am getting these messages:

SQL error. Function: GetSQL Error Position: 0 Return: 8603 - [Microsoft][SQL Server Native Client 11.0][SQL Server]Transaction (Process ID 208) was deadlocked on lock resources with another process and has been chosen as the deadlock victim. R erun the transaction. (SQLSTATE 40001) 1205 Statement:  (......My SQL statement......)

This is a crucial app engine and we are at a work stoppage. I am newer at this job and I am the only programmer, and my skill and understanding is limited. What can I do to prevent the deadlock? Tonight I am going to try to run the process after peak traffic hours and see if it helps.