I know the wifi turns off at some point at night. I suspect that is probably when and why you can't print.
Semi true. The response from the database is on a 30-minute cycle. The wifi may be limited in the middle of the night and the databases might be maintenances during that time as well. But depending on when your store's cycle time is (our's is the :05 and :35 minute marks after hitting the pack station tie), you may have to wait 30 minutes before you see collates. The wifi down time would only limit you during that period.
Granted, if the data base is down it doesn't matter if the wifi works or not. The smart solution would be a local server that pulls the data when the batches are dropped. The data is stored until the batches are pulled and then it's purged for the next group of batches. The local server wouldn't be effected by the wifi and would only connect to the main database when pulling batch/collate information (once or twice a day). But I'm no IT Specialist, so what do I know?