On my last trip my tire presure varied a pound or two but it was consistant with all the tires. I check them in the morning, in the afternoon those that were sitting in the sun all morning were a bit higher but that was no surprise.
On our last trip we did have a tire that started to loose about a pound a day. I carry a amall compressor and would top it off as needed. As luck would have it that tire picked up a piece of metal and went flat. When it was repaired they found it also had a poor rim seal.
The important point is to check, so a low tire does not sneak up on you.