There are a number of things which could be causing you trouble
1. Low power GPU (some trouble, but maybe not everything)
2. Your monitor is running faster than 50Hz, and the TsStream cannot be sped up as it's live TV (the EVR renderer is asking for a speed up of 1.0000217054). Not a lot, but it will deplete the amount of video in the buffer over time.
In this case the second item will cause a slow buffer shrink, which will cause stuttering. Unfortunately you didn't post the EVR log which would have given more information.
There *may* be a version of MPAR tailored specifically for live streams, which will endeavour to solve this problem. In addition the lack of sound problem may be due an errant timestamp on one of the audio packets - this is being actively worked on to see if the problem can be resolved. Without the missing log file it is not possible to say exactly what the problem is.
From the logs, the system "thinks" it's OK from a stuttering point of view, and I can't see anything indicating that audio vanished. But I'd recommend trying the following:
1) Turn off the file existance cache in Configuration->GUI
2) Disable the power scheduler
3) Try using the 1280x720 resolution
2) & 3) should not be permanent i.e. don't leave them, just test using them and see what difference it makes. The server will turn itself off if you disable powerscheduler for more than 10 minutes, so don't panic if that happens .
If the audio vanished during the channel change (you don't say), it could be a bug within MPAR.
Alright... I've done what you said and all worked perfectly. To narrow it down I then tried to turn things back starting with the resolution
and guess what: it reoccured again...
I hope that this does not mean that I have to stay with 1280x720 but that there is another solution.
I have attached all logs.
1) I think you said that it was OK with MPAR disabled - you could disable it only for LiveTV (there's a lot of extra work for the TV stream so it tends to be worse than other media playback)
2) Keep 720p (depends on how good your eyesight is to whether you will notice much - I use 720p as my ION isn't up to higher and the TV is only 1366x768 anyway so having different frequency choices is better than crisper picture)
3) Get a better graphics card
4) Wait and see if we improve anything, a few things are being worked on, but that will require a choice of 1,2 or 3 in the meantime.
If dropping the resolution solves the problem then it's likely to be related to the graphics subsystem... I don't have experience of the HD2000 (My dev machine has the older 3150), so I can't say for sure - but it uses system RAM (possibly giving it a bit more in the bios might help?).
I'd disable MPAR for Live TV for starters, as your TV runs at over 50Hz it's never going to end well . Other media will likely be OK as there'll be less strain on the system.