Well you probably should have done the air sleeve service a couple times now. I usually do mine every 6 months or so. I haven't done it this year because I can't get the damn AVA sleeve off (I need a better strap wrench). So if you don't do the air sleeve maintenance, your lube can dry up and the seals will get sticky. The oil around the schrader valve is probably a slight leak from the seal around the schrader or just a bit of oil blowing out when you attach/remove the shock pump. If it doesn't leak air, I would suspect the latter.
Now, the air sleeve is separate from the major overhaul that needs to be done about once a year to maintain damping performance. This is factory (PUSH or Fox) maintenance that includes changing the damping oil and internal seals and recharging the nitrogen in the damping chamber as well as the full air sleeve maintenance with new air seals. It is almost impossible for the shock to have any damping at all if it were leaking damping oil. If you had a blown shock, you would know it.
As the nitrogen fades, it will require more clicks of rebound to get the same level of damping and when it's really bad, it will start cavetating (that sucking sound). Most people don't do anything with their rear shocks until it's completely blown or making the sucking sounds. Damping performance was probably degraded long before but they may not have noticed because it's more subtle. The overhaul is recommend annually for peak performance though.