EOP, where in europe?
There could be many reasons for the "beep".
Is the character of the beep the same every the time?
Is it from a centre or tower?
Is it from the same centre ot tower each time?
My best guesses from the limited info so far is that it could be:
fist mic operation and a bit of feedback from speaker to mic at the tail end of a transmission;
transmitters and receivers are remote from the site where the ATCO is located and there is tone switching used between the user and the tx/rx site with poor filtering of the tone when the speech ceases;
mic gain too high and feedback when speech ceases.
It doesn't seem like it's meant to happen, sounds more like either a faulty frequency set up or poor operating technique on the part of the ATCO.
Have you subimitted a radio fault report?
Remote diagnosis - always a good game
ST