Water started leaking from a drain cock

Hi,
I just found that water is leaking from a drain cock of a water shut off valve in my basement. It is almost 30 years old valve, but I never had a problem with it. It controls water that goes outside, to my backyard.
Usually, I close the valve before winter and turn it on after winter is over. I did same thing this year. I shut water off in November and I turned it on two weeks ago. Yesterday I found that the drain cock is wet and water is slowly dripping from it. I tried to tight the cock and it got better. But it still very slow accumulates some water.
Replacing the valve would be difficult because of very limited space and lot of wood construction around it. Is there any way I can fix the problem without replacing the valve?
Thanks a lot for your advice.