Yeah, this can happen and it can be managed.
Is the players a recent acquisition?
New signings often have a bedding-in period where they adjust to new training, facilities, coaches and the demands of changing clubs/country etc etc. Normally this resolves by itself and the stats jump back up within a month or two, unless the player is really struggling to settle.
The other option here is to check that the training is actually beneficial for the player, which brings me on to the next (and probably most pertinent) question:
Have you put some thought into their training?
Players respond differently to training and this is to do with many factors such as age, current attributes, determination, hidden attribs, personality. The most important is usually personality (which encompasses hidden attributes).
This could be a very long answer but to keep it concise, make sure the training scheme suits the player. Some prefer hard training, others a little less. Balance it with their playing load. Some also prefer focus sessions, others not so much.
Some players will always whinge about training, this is due to a 'bad' personality. Note that real players will never report as having 'negative' personalities, balanced is as 'low' as they will go.
Is the player jaded?
This is usually the killer and is notoriously difficult to appreciate and then manage in FM. If you are a way through the season and the player has played a large number of games then they are probably jaded which leads to decreased playing and training performance and hence, lowering attributes. Manage tired/jaded players very carefully, some need a kick in the butt but most require rest, managing their playing load and rotating them.
Is the player at an attribute boundary?
Whilst the game reports 1-20 the actual underlying attributes are finer than this. 12.4 reports as 12, 12.6 reports as 13 due to rounding (it's 0-200 under the hood with 55 extra for other stuff, don't worry about it). Sometimes many of their attributes are around this boundary and you can see a seesaw/flipping effect where the attribute deviates by a tiny amount but the game reports as a change in attribute (which it is but its not as bad as you may think). Don't worry about it and in time it will resolve up or down depending on whether the player is trending towards improvement/decline.
What can I do about it?
First port of call is to make sure your training is spot on. This can be easily changed and a little player interaction normally reports on it.
Next make sure your facilities are up to scratch. Hard to solve if they aren't and takes time.
Coaches any good? If they are rubbish you can expect players to decline.
Normally you can interact with a player and tell them their training isnt good enough. You have to be careful but this normally sorts players out. Don't do it to players you need who will get annoyed and want to leave (do you really need that sort of player anyway though?) and be careful doing it to tired and jaded players. Any player with a decent amount of determination and professionalism normally responds well.