Clean and reinstall. They are to run dry with no lube.

Graphite is ok, but I've never noticed a difference in using it or not. Make sure the EOS sw. are clean and correctly gapped.

Burnish the flipper button and EOS switches, clean everything. And make sure there is not excessive wear on moving parts, that might cause the flipper to get stuck every once in a while. And yes, no lube whatsoever.

I had similar issue with Kings and Queens. There was a relay under the playfield that enables power to the coils which caused them to start dropping out even after a full rebuild which would make sense. So you could have all new switches and coils and still would have seen that problem.

Coils and flippers are designed for use without any lubrication. Why would anyone would ever recommend it. My aversion isn't about any extra dirt, but if it needs lube, there is something wrong with the parts. The issue will return when the lube runs out or the broken/worn parts get worse.

Replace the sleeve, they cost about 50 cents. If you don't have a spare or need it in a hurry, clean the original thoroughly and if it isn't worn you can reuse it.
Clean the plunger with a light use of scotch brite.
Check the pawl and assembly for wear.
Replace the playfield flipper bushing. These wear out and eventually cause flipper drag. Another 50 cents, but need a little care to reinstall.

Before you take things apart, manually move the flipper and observe the assembly to make sure nothing is catching or obvious. Sometimes they will catch on the EOS or on a loose wire, or are just worn in a way they move inconsistently.

But your problem is likely electrical as noted above. Misaligned or worn EOS switches are the culprit 90% of the time. EOS switches control the power a coil and could account for the symptoms you describe.

If you need more help, post some pics. There are also many threads on rebuilding flippers.

Graphite is dry lube and won't ever gunk up the parts. But as I noted above, I haven't noticed any difference in using it or not. I would hardly call that a recommendation.

Agreed. If you need graphite for anything chances are there’s something else wrong that needs to be addressed and can be fixed.

Shouldn't have come across that harsh, but saying Graphite is OK to a newbie on what appears to be his first repair, can sound like a recommendation since he asked about it.

My main point was to focus on a proper repair, not a band-aide.

I've had graphite and other dry lubes gunk up solenoid coil sleeves. Clean and dry is the best.

I knew I saw it somewhere. From a Williams manual:
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Well I assumed this one was a Segasa-Sonic, not a Williams.

Hey, as long as you don't try to go Playmatic on us ...

What game are we talking about???

Whenever I have a flipper acting up, it’s one of two things:
Misadjusted EOS switch or,
It could also be a bad solder joint. Check all soldering connections to the coils and the EOS switches.

Following this post since I have a similar issue with a 1968 Domino. Flippers we’re rebuilt and were working well, now the left flipper has lost all it’s power.

Flippers do not have a relay in the circuit. Are you talking about power to the playfield in general?

I wondered about this also. I've never seen an EM from the 60s or 70s with a relay in the individual flipper circuits. Not to say that some manufacturer in the very early days did not attempt to use such a design, but certainly not in a Gottlieb K&Q. Must be referring to one of the relays that turns on power to the playfield???

Check the reset/game over circuit is clean and tight. They can sometime rob power from the flippers.
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From Clay's superb guide: When rebuilding the flippers, it's not a bad idea to replace the coil stops. New coil stops will make your flippers quiet when holding the cabinet flipper button in. Also sometimes the old coil stops are magnetized enough to hold the flipper in the up position. You can buy new stops, or just rotate the flipper and backbox Replay unit coil stops. The replay unit gets very little use, so its coil stops (two coils on the replay unit) should be in excellent condition. Just move the Replay stops to the flippers, and the flipper stops to the Replay unit.

It is always the EOS, and as noted in several replies above, is the first thing to look at.

Based on the condition of that switch, you should rebuild those flippers, aas no one had touched those assemblies in a long, long time.