SRAM's mechanical road shifters have been around for a long time now. They're pretty simple, reliable and effective, but they do have their own unique problems along with their associated derailleurs.
I'll attempt to outline the main issues, hopefully this might help anyone out there with troubled shifting to sort it out.
Firstly, have an idea of what's going on, is your shifting haywire - jumping from gear to gear, not engaging accurately with a gear, or is the bike just not shifting easily and sticking in a particular gear?
Starting with simple stuff:
If the shifting is inaccurate first check your indexing. I like to drop the chain onto the smallest rear cog/sprocket, move the shifter up one click and see what happens, it should click into the second gear/next cog up. If not, adjust the barrel adjuster until it does.
Red arrow: that's the barrel adjuster just in case there's any doubt.
You have a bit of room for manoeuvre, some folk like to bias the shifting up or down, I tend to get it to shift and add maybe half a turn, if it shifts more than one cog you've gone too far.
Ideally put the bike in a stand and experiment until you have a feel for it.
If indexed correctly in one gear it should shift all the way up and down the cassette properly in all gears.
If it doesn't:
Random mis-shifting in sporadic gears: this is most often caused by a mis-aligned gear hanger. It needs checking with an alignment tool, not something that many home mechanics have. Personally I'd buy one because modern gear systems are incredibly fussy about alignment. the hanger and therefore the derailleur has to be parallel to the wheel. Very simple to check with the correct tool, Abbey tools make a beautiful one if you are feeling flush, Park do an effective one if you don't want to hang it in pride of place on the workshop wall. Alignment can be knocked off very easily, a bash parking up outside the cafe is enough. Buy the tool, you'll not regret it, no-one ever regretted buying nice bike tools.
Shifting ok in one direction and not in the other: if your indexing is fine in one direction (usually into lower gears ie bigger cogs) and not in the other, it's likely the cable is sticking or dragging. There are other SRAM issues though which we'll address later.
First, if the inner or outer cable is old try replacing both, they get worn and stick in the cable housing. It pulls ok, but can't release as that's relying on a spring in the derailleur, whereas pulling relies on your great big fit on the shift paddle.
Once a new cable has failed to solve your problems you have officially entered the world of crazy strange stuff specific to SRAM. As above the cable does not like anything that creates "drag". Check the cable run, does it go through under bottom bracket guides? These if plastic can wear and jam cables in a groove formed. Does it go through stupid plastic tunnels to cope with internal routing which wear out and travel round fairly tight corners (Kinesis designed some truly appalling cable routing into some frames).
Have you got the SRAM end cap problem?
The first picture shows a cable taped under the bar tape: won't shift.
Second, cable released and running in a nice straight line: perfect shifting.
Third, a custom made end cap, oversized so that it slots into the shifter, maintains cable alignment as it enters the cable housing which can then follow the bar contour: perfect shifting.
It's easy enough to replicate this with choice of end cap design and some tape, that small angle is enough to mess the shifting up completely. It can be ok for ages and as the teflon/plastic inner wears, what was not a problem, can become a problem. It's simple to test for, just un-tape the bars and see what the shifting does.
Slightly more complex problems:
We've covered the simple fixes now, so onto unusual things.
Occasionally the shifter itself can break, the early ten speed cable brake shifters were notorious. The shifter's cast ratchet actuating bit (name eludes me) could snap, I've seen teeth snap off the ratchet, or more commonly the spool wheel as shown break. SRAM don't make spares but after-market spool wheels are available from Ratio Technology. They're quite simple to replace.
Sticking derailleurs: this causes much head scratching, the symptoms resemble a sticking cable, you can often spot the difference though. If the derailleur is sticking in the bigger cogs on the cassette and not down shifting, try removing the wheel, if the derailleur then shifts fine you may have a sticking derailleur (check the cables as above though as the absence of the cassette can allow the derailleur spring to pull an unhappy cable).
This can happen to any of the derailleurs but is most common with the long arm Eagle MTB models running big cassettes.
It seems to be related to binding of the nylon bushes and insufficient derailleur spring rates along with torsional effects from the chain in the bigger sprockets. I could be wrong.
We've had success curing this by either sozzling the derailleur in mineral oil overnight, or better still but a fairly fiddly job, just rebuilding the derailleur with PTFE lined bushes. We've tried phosphor bronze but I'm back on PTFE lined steel again now.
You may as well, strip the anodising and re-anodise at the same time.
These systems lend themselves very well to running modifications to use newer SRAM components, such as 12 speed and wide range MTB derailleurs with mechanical road shifters. Once you are running these derailleurs with SRAM 12 speed wide range cassettes or Campagnolo EKAR 13 speed systems they do need to be in good shape, although a wonky gear hanger will throw off a ten speed system in a spectacular and puzzling fashion.
I've not discussed the limit screws, chain length or B screw setting, they should be as factory specifications and there are good videos about showing adjustment.