"The doctor is performing surgery on the patient."
Translation:SID HaqtaH Qel.
Both translations are reasonable here.
HaqlI' implies that he is making progress towards a definite ending point, HaqtaH just indicates an on-going action without saying whether it will ever end or not.
Surgery does have a specific end in mind: you know when you're done and you can close up the patient. So HaqlI' would work here as well. But you don't have to use that specific ending and could also say HaqtaH.
By contrast, something such as "She is hitting me" can't be muqIplI' because you can't really say that she is making progress towards a specific end -- she'll keep doing it until she feels like stopping, but there was probably not a specific length that she had in mind at the beginning, where she could measure her progress and say "I'm 40% finished with the task of hitting him".
muqIplI' can make sense given the right context. She's a bully, beating me up, and she'll stop when she's decided I've learned my lesson.
You don't need to be able to quantify your progress to know that it's heading toward a stopping point. "Until I draw blood" is a known stopping point that you don't know how close you are to it until you get there, for instance.
I can't think of a word that couldn't be made to fit with -lI' given the right context. And that's the point: it's not important whether you or I can think of a particular setting for a particular word; it's just important to decide whether the word is grammatical.
Once, long ago, some people were playing Klingon Scrabble at a qep'a', and someone played the word retlhuH. Others objected, saying, "We breathe you" didn't make any sense, and shouldn't be counted as a legitimate word. "That's only because you haven't thought of a context for it," I countered, and came up with a situation in which the speaker is addressing dead comrades who have been cremated, and now they're breathing in the ashes.
So no, I wouldn't tell anyone that verb X never works with -lI'. Someone will come up with a situation in which it makes sense. What I WILL do is tell someone whether situation Y can be expressed with -lI'. For example, if I want to express the idea that I'm running with no destination and no foreseeable end to my running (think Forrest Gump), jIqettaH is appropriate but jIqetlI' is not. But that's not a prohibition on using -lI' on qet; if I'm running to my ship, that's a known stopping point, and either jIqettaH or jIqetlI' are appropriate. What's important is whether the word you use expresses your idea, so you need to know what the idea is before you can say whether the word expresses it. The sentences in DuoLingo have no context by which to judge appropriateness.