Verlustangst (credits to Philipp)
Verlustangst ("fear of losing") is a term which is used especially in relationships. This might not fit your description in all scenarios, because it is really strongly associated with interpersonal relationships, but in these cases it matches the fear to lose someone. It still lacks the idea that it occurs when it is particularly going well.
You composed your noun of an adjective and a noun. The proper way of composition would be to use two nouns here. I cannot explain a rule, because sometimes there are also words composed of an adjective and a noun (such as Schnellzug, and Freibier for instance). I guess in these cases, the adjective has to characterise the noun, which is not the case in your example, because the fear is not comfortable, but it's about being comfortable. So the word would rather be Gemütlichkeitsangst.
I think, the word Gemütlichkeitsangst would not be understood the way you want it, rather it would be taken as "the fear to feel too cozy", maybe somewhat similar to fear of missing out.
What you describe is very much the fear to share the fate of Polycrates. So you could call your feeling Polykratesangst. On the one hand this does nail it, but on the other hand it would be understood by only few people, since Polycrates is not so well known nowadays among Germans, even if Friedrich Schiller wrote a nice poem on him: Der Ring des Polykrates
The bad fate which would be feared by the fear you describe is called Verhängnis in German. The english words fate, doom, also kismet come close to its meaning, but German Verhängnis is always a bad fate, never a good one. So, you could use Verhängnisangst, which would be understood as "the fear to suffer from bad fate". It does not sound very "natural" to me, but this might be due to its nature of a neologism.