Hello Felipe,
Thanks for confirming, that helps narrow it down, and it's helpful to know the local-then-copy approach does work reliably.
As we checked on our end, your account has an Acrobat Pro subscription, so you have access to the Use guided actions feature, which can help automate the local-sign-then-move pattern so it isn't a manual step per file:
Go to All Tools > Use guided actions > New Action.
Add a Certificates/Sign step, and set it to use your Digital ID with prompts disabled so it doesn't stop for each file.
Add a Save step, and set the output location to a local folder rather than the network share.
Save the Action, then run it against your whole batch of PDFs at once. Acrobat will sign each one and save it to the local folder automatically, without you handling files individually.
Once the whole batch is done, do a single bulk copy or move of that local folder's contents to the network share, rather than copying file by file.
This keeps the reliable local-save step, but turns "sign one, copy one, repeat" into "sign all, then move all," which should be much more practical for your volume.
For the full guide on setting up and running Actions, including how to avoid password/prompt interruptions during a batch run, see: Adobe Acrobat Pro Action Wizard.
Let us know if this works for your workflow.
Regards,
Amal