I worked with my professor on a project for two months at the beginning of this year. After a while, I finished writing up the paper and sent it to him to check. He didn't reply. I've sent 5 follow-up emails within the span of 3 months after that with no reply. I am afraid to send another follow up email (the last one was a month ago) because I don't know whether he wants to continue with this project anymore. Should I just give up? or start sending more follow-ups but at a higher frequency?
Email is obviously not succeeding, so contact him another way. Phone, postal mail, visit his office, etc. You may also contact his department chair and ask if they know of any reason why he wouldn't be answering emails.
I don't know whether he wants to continue with this project anymore.
Even if that's the case, you have every right to be told that directly. Ignoring your emails would not be an appropriate professional way for him to communicate that to you.
I see two possibilities that haven't yet been mentioned, and can think of several others. But it can all be cleared up with a personal visit.
The first is that your mail is being flagged as junk and relegated to a junk folder. Mailers can be weird about that and one of my regular correspondents always winds up in my junk folder.
But the other possible reason is the nature of your email. You don't say whether you explicitly ask for feedback or just assumed you would get it. If you don't ask, it is possible that the professor is treating your mail as "for your information".
Other possibilities include illness or overwork, etc. But the way to get real feedback is to meet in person. You can ask for "next steps" or "what is still needed".
Check very nicely with the department secretary. The office staff often know what's going on with various professors and might have suggestions about how to get a response.
Yes, you can send too many follow-up emails. How many is "too many" depends on the importance of the issue. Publishing a paper is very important, so I would say that you cannot send too many. However, you could send them too frequently. Try once a month. Don't give up.