No 3 beep notification in the earpiece of an incoming call

I had the same problem and the cause was the handset lifter and not the earpiece--if the ringtone is too low at the lifter, it won't be detected and transmitted to the earpiece. Cranked up the ringtone and everything is fine.

If that doesn't take care of the problem you might look at whether or not you're using custom ringtones which might cause a problem. Switch them back to the defaults and see if the problem goes away.

One more thing you may want to check is whether or not the lifter sits right above the speaker for the ringing of the phone.  If it doesn't you need to install the mic attachment that comes with the lifter, and center it over the ring speaker.
Also keep in mind that the beep beep beep doesn't happen until the end of each ring cycle (i.e. phone goes riiiiiiiiiiiiiiiing then you hear beep beep beep during the silence until the phone rings again).

Use the included external mic to get it to Beep. A more interesting problem is to get it to stop Beeping. I can't get mine to stop while on speakerphone. Talking to support revealed there is no on/off switch. Turns out that the feature only works with the lifter. The lifter comes with the external mic but also has one included just on the bottom just under the actual lifter arm. If you're willing to void the warranty to stop the beeping permanently you can clip the wire to it, no more beeping! I have no idea why they haven't included an on/off switch for the bleeping beeping. I'm sure with a little ingenuity and radio shack you could make one.

Something interesting was happing with mine;
Whenever I cough, I hear the "bee-bee-bee" like I've got an incoming call.  Any loud noise near the phone will fire it off.  Not sure what the correlation is, though, since I would assume that those beep notifiers are being generated by the headset's base station detecting an incoming call.  But maybe not, maybe it's based on the sound of the phone ringing?  If that's the case, the suggsestion I offer would be to turn up the volume on your actual phone, and see if making it louder will fire off the bee-bee-bee.

Same problem here. Increasing ring volume cured it. Also, the coughing does cause a similar enough noise to make it bee-bee-bee. (Also, blowing down into a bottle of soda, like we did when we were kids, causes it to bee-bee-bee. LOL)

I've discovered there is a significant delay time from when the phone rings and the headset gives the beeps, although the time varies.

My theory to this is that since it is a wireless setup, as with all wireless systems, there may be intermittant interference which we can't detect between the base and the receiver.

I believe sometimes it takes a second or two or three for the earpiece to either wake up or hear the signal from the base or hear ringer noise through the microphone.

Regardless, I'm patient with it and I compensate. No accessory device on the market is perfect all the time; there's always the need for the user to adapt to how the device functions.