Allay will continue trying to pick up items for forever if its assigned with any item and has already picked up a partial itemstack with nbt of same type. This will cause it to get "stuck" in this "trying to pick item" loop. Work around is to go near allay itself so it can empty out it's inventory. 

I will be using white banner and ominous banner as an example but this works for any item out there which has nbt. 

Steps to reproduce: 

1. Assign allay a white banner
2. Throw some white banners on the ground. (amount less than 16)
3. Throw some ominous banners.
4. Move back. 
5. Observe allay getting stuck trying to pick ominous banners.

Possible fixes for this behavior can be to have a timeout in allay pickup task. Which when over, allay drops the items to its target player/noteblock