That's a good question.
The answer, I think, is that not only acts as a unit. I can't think of another adverb which can take not in this way.*
The regular form I didn't only lose all my money is also possible.
*Constructions with not + adverb are common when there is no verb, as in "Do you always go that way?" "Not always"; or "He finished the job, but not quickly". But when there is a verb, the negative normally goes to the verb in the usually way "I don't always go that way"; "He didn't finish quickly".
Edit: I have thought of one more example: not infrequently. But neither often nor frequently works this way.