Although my shop does not ask for a deposit, I would not be offended if they did and would pay it. They are taking their time and money to see what is wrong with a machine and if the customer decides they do not want the work done, then they at least have the deposit monies.
On the other hand, there is humor in what you say about not bailing out your baby. However, not everyone can bail out their baby by the amount of machines left in the shop for months on end. Go figure!
When I had my diamond wedding ring band squared off, I had to leave a deposit. Balance was paid when I picked up the ring. Considering the price of gold, the $50 deposit was minimal. Happy to pay it.