Some Background: I was hired for an engineering position while in school for both summer internships and a full-time position after college. My first summer internship starts in 2023.
Recently I was hired for this engineering position and have started to get ready for my first summer internship with this new company. I've only met my boss briefly when I was accepted to the program a few months ago, so he doesn't know me very well. As a part of this program, I get invited to a number of things, online seminars, help recruit more applicants, etc. but recently I was invited to apply for an opportunity in which I get to spend my summer internship abroad working for a partner research institution. This was very appealing to me as I was denied my only study abroad opportunity this past spring due to pandemic related concerned.
Anyways, I reached out to my boss via email and sent him all the information. There is a requirement that my manager needs to provide a brief statement (1 page) of why this experience for me would help meet the goals of our group. It doesn't need to be an essay filled with personal anecdotes. After about 8 business days without hearing back (to be fair, my boss was out for a few days) I sent another email to reiterate my interest and ask for his help/blessing to apply. After a few more days of silence, I finally called. He picked up and told me that someone else was supposed to have contacted me, and will reach out the next day. The next day comes and goes without a peep on the matter, so I try to contact the other person via phone and email (whom I've also met once) and have not heard anything.
The deadline for this is early January so I want to be persistent, but I don't want to be annoying. Should I keep sending emails or should I just leave it alone? Also, some people are telling me that this silence may imply that they don't want me going, which is fine, I'd just like an answer.
PS: There will probably be more opportunities like this in the future, but I'm not positive.