The end of the stem, where you locate the washer, should have a sort of depression or 'washer retainer' at the end. It is sorta shown in this picture (left side, bottom):
Sometimes that wears/corrodes away. The result is that the rubber washer, under compression, sorta squishes out, gets malformed, and wears prematurely. One symptom of this the 'extra turns' you describe as necessary to get the thing to shut off.
The sell replacement washer retainers. You need to chip away the remains of the original, install a rubber washer in the replacement retainer, put the washer screw through both parts and tighten.
This repair, in my experience, is temporary and will give, at best 6 months or so of service before it, too, fails and a new stem much be purchased. A new stem, by the way, ought to last as long as the original ..... assuming you can find one and the price is less that $50 to $100 or more.
There is also another possible cause for premature wear ..... even wear in as little as a few days. A badly worn washer seat (that part of the faucet body against which the faucet washer seals). Some faucets have replaceable seats. If yours does, replace it. On other faucets, the seat is fixed in place but can be smoothed with a special tool (valve seat reamer). Just be careful if you use a reamer. It must match the profile of the original seat.
In the end, I agree with the poster, above ....... replace the faucet.