I don't think a tap alone is going to fix it. If it has already shed the blade once, that tells me the threads are stripped and a tap isn't going to remake the threads.
A longer bolt might reach new threads deeper in the shaft, or drill the shaft deeper, tap deeper, and use a longer bolt. But left hand bolts, especially metric, are hard to come by and expensive.
I've looked at the parts and have a new alternative. The shaft is ~$68 IF, and that's a big if, it's available. The bearings, takes 2, are ~$18 each. Apparently these are sealed bearings, so replacing them would renew the bearings and seals. If you can get the pulley off the shaft, remove the spindle from the deck and have the dealer replace the shaft and bearings. If you can't get the pulley and spindle off, take the deck to the dealer. Ask the dealer if he can get the shaft and how much he would charge to do the work.
I'd appreciate comments from others.