"I suppose not" sounds much more natural in English. Your suggestion is grammatically correct, but we just don't say it like that. Darn English.
Actually that's not quite true, it depends on the question. 'Not' is more common but some questions might more accurately be answered with 'I suppose NO'. The simplest being ' Tell me is it Yes or No'.
In English we say "I guess not" so we will see whether this will be accepted by DUO in the future.
In Italian, sì e no are adverbs, standing in for (non) così è.
No = non così è doesn't modify supporre, rather it is what you suppose - the verb's object. But you can't have verb2 [see @desifromitaly below] or an adverb as the object of verb1. So you add a preposition to make it a phrase, and with supporre and many other verb1s that is di.
In English yes and no are not adverbs and scholars don't agree on how to class them. Presumably that's why, rather than "yes" and "no", we say "so" and "not (so)".
If you add a verb, you can say "suppongo di non...". For example: "suppongo di non poterlo fare" , "suppongo di non essere in grado", "suppongo di non riuscirci", ecc. But if you don't specify anything, in Italian you have to say "suppongo di no" ("suppongo di non" is not correct).
The English language is very difficult. For me, the negation of "I suppose so" is "I do not suppose so" - but that was marked wrong.
To be a bit pedantic, not to suppose so is not the same as supposing not if in fact you suppose nothing at all. Your suggested wording actually means that you are not making a positive supposition but it does not mean you are making a negative supposition. This is because there are three possibilities rather than two and you have only negated one of them.
Report it. That's a valid translation. Although, if I was to say it that way, and I have, I'd most likely use the "don't" contraction instead of "do not".
The English is fine. It was just Duolingo pointing out where the negative is in the sentence - it's not on the verb. In the English, it doesn't make a difference in meaning, in my opinion.
I said, "I don't suppose so" which is exactly how I say this phrase and it was rejected. Any reason why, or should I report it?
Wouldn't this be more like: Non suppongo di si.
The meaning isn't really different in English, but the translation isn't so precise. And Duolingo does like precision during the exercises.
As much as I understand the benefits of literal translations on Duo (that is, to give you a proper feel of what the sentences convey in Italian), hardly anyone casually says, "I suppose not" in English.
It's formal, almost stilted language. I reported it for it to be fixed, but we'll see how much that'll happen.
"Non suppongo." = "I don't suppose."
"Suppongo di no." = "I suppose not."