I've used some "junk" bits that I've since disposed of but I still have some Hitachi, some DeWalt, some Bosch and a few Makita bits from bit sets I bought just to get a supply of Makita Phillips bits. Any brand other than Makita gives me "fits"...or, rather...unfits. As Larry mentioned it could be the bit holder. I have a Milwaukee 6580-20 that had the same problem until the bit holder was replaced under warranty.
Thanks to all who contributed to this discussion.
Max