Can someone explain the difference between these two to me?
長い間日本語を勉強しなくて、下手になりました
長い間日本語を勉強しなくて、下手になっています
The way I understand it currently is that the first one indicates that at some point in time, my Japanese has become rusty, whereas the second one indicates my Japanese having reached said state (is in said state currently) with the process (of deteriorating) still continuing, but I'm aware that I may be entirely wrong and the second option can't even be used.
下手になりました and 下手になっています may be used interchangeably in some situations, but they are different.
下手になりました is "became rusty" — it simply refers to what happened at some time point in the past. It does not necessary mean your Japanese is bad now. For example, you may have restarted studying Japanese last month and your Japanese may be good again now.
下手になっています is "has become rusty" — it describes the continuation of state because なる is basically an instant state-change verb. This does not mean the process is still continuing, but rather means the deteriorating process happened in the past and its resultant effect is present now. That is, your Japanese is bad now.
Compare:
If you want to say you are still in the deterioration process ("is becoming rusty"), you can say 下手になりつつあります or 下手になってきています.
EDIT: The teiru-form can mean two things, and you can "force" the progressive reading using だんだん (gradually), どんどん (increasingly), 少しずつ (little by little), 毎日 (every day), etc., as pointed out by aguijonazo. どんどん下手になっています means "is becoming rustier and rustier".
(By the way, 長い間勉強しなかったので or 長い間勉強せず is better than 長い間勉強しなくて in this context.)
