Remind professor of email a second time? Disclaimer: I know there are some similar questions around. However, I don't feel like the answers there suit this situation completely. This is why I am asking.

Some backstory (not necessarily important, but maybe of interest, just to give the complete picture): A student of mine was talking about a thesis (undergrad, so a relatively informal project of 1-3 months) at an external research facility. The professor there answered her first few emails in a positive way, they started discussing timetable. Professor says, he's away for some time next year. Student makes suggestion for time to work on the project. Professor answers, says he forgot to think of some traveling he had to do during that time. 
Now, student proposes another time for the project, later in the year, when the professor said he was at the institute.

Now the problem: Professor doesn't answer anymore. Student waits 2-3 weeks, sends a friendly reminder, just as recommended in a lot of the answers on here. Waits another 2-3 weeks - no answer. Student seems to be a bit insecure now, emails the secretary of the professor saying she might have missed the professor, maybe he was absent, asks when he's in office. Gets an answer, saying he is back in office at date XY, not really clear about whether the professor was absent before or not. 

Now she came to me, asking whether I had any experience with this. She tells me the story I told you here and says that he feels it is rude to remind a second time but she a) might have missed the professor, he travels a lot, so there's that possibility and b) she also feels like the professor would send at least a short notice if he decided to cancel the project. On the same time there is a time problem because she has to find another thesis at some point if this one doesn't work out. However, contacting someone else might result in an awkward situation of having to cancel on of the projects in a late stage of preparation. She also really wants to work with the professor, he was no. 1 on her list. 

I - sadly or luckily - have experienced no situation like this. But maybe there is a higher ranked academic (I am only a grad student myself, her tutor) or someone who had a similar experience here who can give his opinion on that. I genuinely feel bad for her and want to give her some good advice. 
Thanks a lot!
I would track down the professor in person, coordinating with the secretary if necessary. People get busy, and dragging out the email chain seems unproductive. If the student meets the professor in their office, this can probably be settled in 30 minutes. Assuming the professor tends to be very busy, I would email the secretary and ask when the professor has 30 minutes free for a short meeting.