It's permissible to drop the hai in negative constructions of the present habitual and present progressive tenses.
According to my experience as someone who has learned Hindi from many sources and lived in India in Western Hindi dialect areas (and as evidenced by Duolingo as well), it's not only permissible but it's also very common and natural. According to one native speaker on these boards from the Eastern Hindi dialect area, it is not very common.
Hi Sam, The short answer is that "You just don't" :) That "hota" thing happens with the verb "to be". The distinction is just between two forms of expressing "to be:, i.e. "hai" and "hota hai," wherein the latter (as you know) is for generally applicable facts and laws.
With the other verbs (i.e. other than /honā/ "to be"), don't worry about it.
There IS such a thing (as I think you're suggesting) like "ve taṛte hote haiṁ". But that is really "advanced" grammar that Hindi courses seem to rarely reach :o In that case, the /hote/ contributes an added connotation of habitual-ness to the action. It reminds me in English of the way someone might say (especially in African-American dialect(, "He be going there every day" as opposed to the more common "He goes there every day". It's like you want to emphasize the doer is in this perpetual or habitual state of doing the thing.
हाथी उड़ नहीं सकते । You'll see this type of construction when you get to the Modals skill.
It should be noted that, just as in English, it's ambiguous whether you're really saying "they are incapable of flight" vs. "they are not allowed to fly".
I'm just another student like you, so take what follows with a grain of salt.
In English, your phrasing would have to change somehow to express "possibility/impossibility" over permission. E.g. "elephants are unable to fly", "elephants do not have the ability to fly". I expect you'd have to do the same in Hindi.
This is a variation on the Wiktionary sample sentence for सक्षम:
हाथी उड़ने में सक्षम नहीं हैं ।
Or, more likely since you're expressing a general "truth":
हाथी उड़ने में सक्षम नहीं होते हैं ।