As with all over the air (antenna) signals there is going to be some signal loss. You are using the worst type of signal acquisition for a high quality receiver to process. With over the air signals you can have slight interference from radio's, cell phone towers, air traffic and sun outages. In fact we just had a series of sun outages a couple of weeks ago...
If you want a perfect picture and sound quality sounds to me like you need to invest in satellite or cable...
I have DirecTV HD and it is great. They broadcast in 720p and 1080i signals on HD channels and it looks and sounds great.
EDIT - Just giving you options to your problem of sound dropping out. It is usually caused by signal loss when using an antennae. Just for a split second will cause you to lose sound. I say the antennae because you say it doesn't happen at all when watching via other components hooked up to the Denon.
Usually a problem with the receiver will repeat while in operation...so that kinda rules that out.
It could be just the modulation of audio signal from those stations that is out of sync or under powered a little?
One more thing is the length of your cable from the antennae to the receiver. If it is over 100' you are going to start losing some signal due to resistance?
>EDIT 2 What do you mean the tv sound is still there when the receiver drops out? You should not have any sound coming out of the tv while using the receiver. It is processing the audio and sending it to the surround speakers. The tv audio should be turned off always with a home theater system. Do you have the antennae signal going to the Denon first? You should have the antennae input to the Denon unit and then audio output goes to the speakers and the the video out goes to the tv video input. Is that how you have it hooked up? This should be hooked up to any source input in back of the Denon that has the coax input and output.
>>EDIT 3 WOW...I have tried to be nice but your not very bright are you? I am the expert here and you are wrong about your Denon unit function. This Denon AVR4308CI is a high end state of the art home theater RECEIVER ! ! ! I looked up the specifications and you are so wrong about how you have it hooked up. Sorry if you want to waste $1500 on a top of the line receiver and have it trying to process 2 channel sound from the tv you are crazy...
It is built to take the TV antennae signal and process it via COAX input, component input or HDMI inputs. Your unit has 3 COAX inputs just made for that antennae hookup! ! ! PUT THE FREAKING ANTENNAE COAX INTO THE RECEIVER AND USE LIKE ITS MEANT TO BE USED THEN THE COMPONENT or HDMI VIDEO CABLE OUT GO'S TO THE TV SO IT IS IN HD... Your unit probably has internal switching so you don't even have to hook up another video cable. Just switch input sources on the remote to which ever source you plug the antennae coax into and it will use the cable that your already have hooked up.
NOTE : TV's do not have built in audio dolby digital tuners and do not have surround signals going out. It is just sending 2 channel audio to your 7.1 channel receiver. Since you obviously don't know what your RECEIVER is for here are the features below...
Sorry to be so blunt but you need to listen to me....I have a similar system hooked up and have been working with surround sound systems for 14 years.
EDIT 4 - You say you have digital broadcast problems with the sound so that means your antennae signal should be digital ready so try to run it through the Denon first. It can work that way since all receivers are built with pass through video. How hard would it be to try what I am suggesting? If you get nothing but static then I am wrong but at least you tried to hook it up like I would have the first time and failed.
I still think your over the air digital signal will pass through the receiver and the audio will be recognized. All receivers are built to receive all video and audio signals. The receiver is built to receive a video signal via coax, component cable or HDMI then send it back out via the main HDMI cable to the TV. Your unit even converts all video signals to HDMI so it can use just one HDMI cable out to the TV. It doesn't matter if your sending a VHS signal via a coax cable to the receiver...it is going to remaster it and send it to the TV via the master HDMI cable. All you have to do is switch input sources on your remote to access the different input components. (DVD, Blu-Ray, VHS, TV, Cable TV, CD) You should be able to hook all those units up to the Denon with just one master HDMI cable out to the TV. That's how they designed it to work....you are bypassing the the receiver for no reason. Why don't you try it? Experience was just to let you know that I am not 20 yrs old and that I am truly trying to help you sort out the problem not prove you wrong.
Good luck with all of this...sorry I can't help you like I have helped so many before.
General Features
Color Black
Surround Modes DTS-HD, DTS NEO:6, DTS ES Matrix 6.1, DTS ES Discrete 6.1, Dolby TrueHD, Dolby Digital EX, Dolby Digital / AC-3
Video Conversion to HDMI
D/A Converter 24-bit/192kHz
Remote Control Illuminated Full Function
Stereo Power Rating 140 Watts x 2
Surround Power Rating 140 Watts x 7
Tuner XM Radio Ready, HD, FM, AM
Inputs / Outputs
12V Trigger (2) Rear Output
Antenna HD, FM, AM
Coaxial (3) Rear Input
Command / Control (1) DENON LINK
Composite Video (6) Rear Input, (2) Rear Output
HDMI (4) Rear Input, (1) Rear Output
Multi-Channel (1) 7.1 Channel Pre-Out, (1) 7.1 Channel Input
Multi-Room Rear Output
Optical (3) Rear Input, (2) Rear Output
RJ45 Ethernet (1) Rear Input
Satellite Radio XM Radio Ready
Analog Audio / Video (8) Rear Input, (2) Rear Output
Component Video (3) Rear Output, (3) Rear Input
Monitor Output (1) S-Video, (1) HDMI, (1) Composite Video , (1) Component video
RS-232C (1) Rear In/Out
S-Video (6) Rear Input, (2) Rear Output
Speaker Terminals 5 Way Binding Post
USB Port (1) Rear Input