The deck joists underneath this wood decking will
suffer from serious problems eventually because the deck was built too
close to the ground and there is a small space between the deck and the
The space between the deck and the house is not that bad of an idea as long as it is at least three quarters of an inch away from the home.
If the gap is any larger you could have rodents nesting underneath your deck, if the gap is in a smaller, dirt and leaves will accumulate in between the floor joist and the house siding. This of course will cause the wood siding and wood deck joist to start decomposing.
This deck is sagging because it was built too close to the house will need to be repaired.
From repairing decks like this before this is not going to be an easy job. You will have to remove almost all of the joists or cut a straight line down the next closest joist from the wall and then removed the small section of wood decking. After that you can't repair the sagging joist and reassemble the decking.
Sagging wood decks are never that easy to repair when they are built right on top of the ground.
Sagging decks that you have access to underneath can be repaired a little easier.