Ask what the contract stipulates (or in other words, you are severely lacking information to answer the q).
If they insist an answer - and I understand that they make a solution impossible, the app fails, everything has been tried, the supplier won’t update it - then either you offer alternate software or you consider how much it would cost to keep the customer and perhaps let them go
In any case, I would also tell them that either we have a monopoly position and the customer is stuck with us, or there is competition who don’t appear to have their software fail so in that case I don’t believe that everything has been tried yet to fix ours
Also after rebooting? Sometimes it can be a tab in your browser which you forgot about. Some sites also automatically push you video ads over the text. Don’t know which browser you use but on some you can see if a tab is playing sound or not