May I know which Cypress Type-C host you are testing? Is there part number of this?
May I know what's part number of Ultrafine 4K monitor you were testing?
Is there any Type-C to DisplayPort dongle between Cypress Type-C host port and Ultrafine 4K monitor? Which part number of this dongle if there is?
Do you have CC negotiation log based on this case?
The Type-C host is desktop option AIC & use CCG4, Parts number is CYPD4225-40LQXI
The LG ultrafine 4K monitor as below link:
There are Type-C cable direct connection between type-c host & monitor.
Due to this is end user feedback, so no CC log can provide.
Without CC log, it is difficult to analysis the root cause of the resume issue. Meanwhile, Either Notebook or Monitor is the terminal products(with Type-C solution), you may want to contact the products vendors reporting the compatibility issue and get support from them.