Is it incorrect to say "I couldn't catch that" when referring to missed conversation?

A friend of mine who speaks English as a second language asked me if it was correct to say "I couldn't catch that" when referring to just having missed a part of a conversation, e.g. a phone call. My initial response was "It's normally 'I couldn't hear that' or 'I didn't catch that', but not 'I couldn't catch that'", but upon further thought I wasn't sure why that was the case; it seems grammatically correct, similar to "I couldn't hear that", but it feels unnatural to say in that context. Is there actually a rule in place here, or is it just a highly uncommon usage?

Solution 1:

My initial response was "It's normally 'I couldn't hear that' or 'I didn't catch that', but not 'I couldn't catch that'"

That is my response also.

"Could" in this case is the past tense of "can" and expresses an inability. But normally, the sentence "I couldn't hear that" would be followed by, for example "because of the noise in this room", or because of some other exterior cause that explains that your temporary inability is abnormal.

On the other hand, 'I didn't catch that', is the negative past of "to catch." and is complete in itself because it is a common experience when the speaker speaks indistinctly or if his speech is impeded by a physical, passive, obstruction and the cause is obvious, e.g. he is speaking from behind a door.

PS: When giving examples of verb forms, it helps if you keep the same verb.