It sounds like the original coating was too thin. When you use a silvering solution, there are two types of silver deposited. One is a brown precipitate. This is silver, but not the desirable bright adherent silver film that coats the mirror. To avoid getting it on the mirror surface, the solution can be agitated, or the mirror silvered face down. A good deal of the silver ends up being wasted as the brown precipitate, which is the result of the silver ions getting reduced too quickly to form a continuous metallic coating. It cannot be avoided, as the reduction is done in solution.
The new silver film should be burnished, and it can be made more durable by applying a lacquer. One way to do this is to put the mirror on a record player turntable, rotate it slowly and apply the solution with a brush. Perspex chips can be dissolved in a solvent like ethyl acetate, though the solvent must not be one that evaporates too quickly, before the turntable has helped in spreading the solution.
Any trace of sulfur in the atmosphere will form a yellow-brown deposit of silver sulfide upon the surface, and it sounds like this happened in your case. It may be that in your location in Italy you have some sulfur dioxide or hydrogen sulfide in the atmosphere, in which case aluminising will be a better option. (Aluminium is less suited to observatories near the sea, unless it is overcoated. Chloride ions cause pitting corrosion of the film.) As an aside, I once aluminised a mirror myself. Chemically cleaned, placed upside down in a small vacuum chamber and suspended over a heating element upon which small turnings of aluminium had been hung….. Very interesting to do. The inside of the chamber gets coated as well, of course. 45 years later the mirror is still shiny!