I designed and was the general contractor for our 12 year old home. From the front the house it appears to be a split level entry and with the slope of the land the rear appears to be a full 2 story, with 2 sets of patio doors at each the upper and lower levels. It is L shaped and in the L is a 16x16 concrete patio that is tilting towards the house. Now this isn't as bad as it first sounds because, this point, at the rear of the house is slightly below the lower (or basement) level and therefore doesn't possess a problem for water to enter. It does however keep water and snow in this pocket with the patio now algae green.
Answer:
If it had good drainage under the slab, you wouldn't have the accumulation of water there so you might give serious thought to correcting that. Unfortunately, it may mean breaking up the patio, adding fill and grading it properly before putting in a new patio.
