As someone who works in (completely unrelated) support, the numerous emails may be a contributing factor to your problem. Most support is done using last contact as the priority. When you send a new email, you're resetting that counter and bumping yourself to the bottom of the queue.
This was a problem we had with a /particular/ support system (Kayako) and we've since resolved it (with ZenDesk) but if they're using something silly like Kayako, that might be the reason.
Also, if they have a phone number, use it.
Not justifying what they do, just trying to help you work them out.
Hmmm, that might explain why Pebble (the smart watch) support had this super passive aggressive sounding "if you keep emailing us about the same issue, we'll put your case to the bottom of the list" instructions.
Not the message you really want to be sending your already disgruntled customers - "Do I mail them and check to see if they even got my email which hasn't had any response in two weeks, or will that just put me _another_ two weeks further down their already abysmally slow response queue?".
This was a problem we had with a /particular/ support system (Kayako) and we've since resolved it (with ZenDesk) but if they're using something silly like Kayako, that might be the reason.
Also, if they have a phone number, use it.
Not justifying what they do, just trying to help you work them out.