Dear Ignasi, a very common question that sooner or later comes up to any collector - or simple owner - of at least one vintage watch.
And even more so to Heueristis, as some of the mid-70's specimens - especially Autavias - have a rare gift of shedding their lume material.

I agree with Mark most, and therefore with your watchmaker: if it's a really vintage watch (e.g. a '60's Carrera or an 1133B), and not so much of a wearer, then leaving it as is now is by far the best option and surely the safest. Originality in such watches is the great part of the value.

On the other hand, if it's a watch of not so high financial or affective value, and you want to use it often and don't care too much about it (well, you will still care a lot but no SO much!), then reluming by a very reputable watchmaker is an option to evaluate: think e.g. of an '80's 510.5xx that may also have its fair share of knocks and dings.
But you have to be careful in picking the right person - of course any of the 'big names' here will suit.

Hope this may help you in your decision somehow.
Cheers,
Fabrizio