I'm not an HTC user so I'm not familiar with the Sense UI.
Just make sure that your ringtone is not set to silent (choose a different one if it is).
Try and test if you're able to hear audio with games and audio/video files.
There could also be different settings for audio (ie: ringtone, system, media), make sure you're adjusting the ringtone.
Does it happen for both incoming calls and sms?
If it only happens with sms try and install other sms apps from the playstore.
Other forums (could be helpful or not):
http://androidforums.com/desire-support-troubleshooting/82002-desire-getting-missed-calls-but-phone-...
http://www.askmefast.com/MY_HTC_DESIRE_PHONE_HAS_DECIDED_TO_STOP_RINGING_if_someone_tries_to_ring_al...
