"We need breathing room" and "Explore strange new worlds" are the 'daily' exploration missions that give you Dilithium for completing 3 'explore' missions in a sector. First, you have to have the explore tour mission, then you can complete it, if you have remembered to get the second quest (breathing room and strange new worlds) you can turn that in at the same time for 1440 dilithium.
With me so far?
The problem is, Breathing Room and Strange New Worlds are on a count down time from the moment you received the mission. Ordinarily that wouldn't be a problem, except that it generally takes up to an hour or so to do the three missions. (this is assuming you are not getting around the system by just leaving the planet without doing the missions that you don't like) The result is that day by day you can't start the missions, or at least you can't turn in the missions until later and later in that day, depending on how long it takes you to complete it.
What I suggest is that it be put on a 22 or even a 20 hour timer. The racing quest is on a 20 hour and that should show you the benefits of that. The winter race only takes two minutes to complete too! If a 22 or 20 hour timer is used, then you will have the time needed to do the missions and still turn them in without the pressure to do it quickly so that the next day won't be too late in the day.
I was told there were threads about this, but honestly I searched through the last 5 or 6 pages and found nothing, so I figured it was time to bring it up again. '
A 22 or 20 hour timer will not change significantly the amount of dilithium a player can get. It won't change how often you do the missions, except for possibly making players more likely to do them without the timing issues.