I am a little unclear as to how the third program is being added - are you trying to record a program when two others are already recording, and you get no warning? Is the receiver just making a recording on it's own? If you get the warning, what do you do?
All I can think of now is that there is a rouge timer that exists but for some reason is disconnected from the guide. If you are sure you usually have about 8 days of guide, then I would do the following;
Having tried a memory dump, and resets, etc... I would delete all timers. Then, do a reset either by the power button or unplugging it. Then, make sure there are no timers listed, or anything showing in the schedule to be recorded, or skipped etc... If a timer or something is still scheduled shows up, that might be the issue.
If there is nothing, next I would add timers. Try not to add time before or after it starts for now. Be on the lookout for times when you are trying to record more than two shows, another words know that you are adding a third program before you even try so you can be watching for the warning screen to prioritize. Do you get that screen?
If you get the screen and everything is working as it should, now go and add time before or after the show starts if you usually do that.