I have a strat with vintage Fender Ping tuners (I am pretty sure about this, but the vintage gotoh look similar). The tuner for the A string doesn't hold as well as the others. Is there a fix for this?

Remove the tuner from the guitar and flip it over. You will see two tabs on the underside of it, one on the top and one on the bottom, crimped down against the housing. These tabs are holding the box cover on. Pry these tabs out to straighten them, thus allowing the box cover to be removed from the housing.

I must warn you though, it is very easy to stab yourself in the process of trying to straighten these tabs.

Once the box cover is removed, you can ascertain whether the gear simply needs to be tightened on the shaft or, the components have intrinsically too much play. If intrinsic play (including possibly a damaged component) is the culprit, you'll have to replace the whole tuner or at least, all the guts.

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You dig?