I have conducted a study on the chances for ships (my test used curraghs) to sink in water (my test used only ocean, though I am pretty sure the chances are the same for sea). I used 50 curraghs (unless otherwise noted) for a non-Seafaring civilization (Rome) and 50 curraghs (unless otherwise noted) for a Seafaring civilization (England). Below is the raw data and a couple of graphs. If you have any questions, feel free to post in this thread. My conclusion is at the bottom of the thread.
All tests done with Conquests, v1.22.
Notes: % that survived a second turn in water is a % of the ones that survived the first turn. For example, if I lose 10 of my 50 curraghs, I have 40. 80% survived the first turn. If I lose 10 more curraghs the second turn, I lost 10 of my remaining 40, so that’s 75%.
Data
Plain Survivability
Chieftan
-Non-Seafaring-
Curragh in Ocean: % of survival in turn 1 (% of survival in turn 2)
First try: 54% (% that survived a second turn in ocean: 33% (this one moved a tile))
Second: 46% (% that survived a second turn in ocean: 34.7% (this one moved a tile))
Third: 32% (% that survived a second turn in ocean: 56.25% (this one stayed in the same ocean square))
Fourth: 56% (% that survived a second turn in ocean: 46.4% (this one stayed in the same ocean square))
Fifth: 48% (% that survived a second turn in ocean: 54.2% (this one moved a tile))
Averages: 47.2% for first turn – 44.91% for second turn
-Seafaring-
Curragh in Ocean: % of survival in turn 1 (% of survival in turn 2)
First try: 70% (% that survived a second turn in ocean: 68.6% (this one moved a tile))
Second: 72% (% that survived a second turn in ocean: 61.1% (this one moved a tile))
Third: 72% (% that survived a second turn in ocean: 86.1% (this one stayed in the same ocean square))
Fourth: 76% (% that survived a second turn in ocean: 81.5% (this one stayed in the same ocean square))
Fifth: 74% (% that survived a second turn in ocean: 75.6% (this one moved a tile))
Averages: 72.8% for first turn – 74.58% for second turn
Monarch
-Non-Seafaring-
Curragh in Ocean: % of survival in turn 1 (% of survival in turn 2)
First try: 50% (% that survived a second turn in ocean: 36% (this one moved a tile))
Second: 60% (% that survived a second turn in ocean: 53.3% (this one moved a tile))
Third: 48% (% that survived a second turn in ocean: 37.5% (this one stayed in the same ocean square))
Fourth: 50% (% that survived a second turn in ocean: 64% (this one stayed in the same ocean square))
Fifth: 46% (% that survived a second turn in ocean: 39.1% (this one moved a tile))
Averages: 50.8% for first turn – 45.98% for second turn
-Seafaring-
Curragh in Ocean: % of survival in turn 1 (% of survival in turn 2)
First try: 82% (% that survived a second turn in ocean: 80.4% (this one moved a tile))
Second: 66% (% that survived a second turn in ocean: 72.72% (this one moved a tile))
Third: 76% (% that survived a second turn in ocean: 76.3% (this one stayed in the same ocean square))
Fourth: 74% (% that survived a second turn in ocean: 72.9% (this one stayed in the same ocean square))
Fifth: 82% (% that survived a second turn in ocean: 60.9% (this one moved a tile))
Averages: 76% for first turn – 72.64% for second turn
Tests of Terrain and Ship Type
Regent
-Non-Seafaring-
Galley in Sea: % of survival in turn 1 (% of survival in turn 2)
First try: 60% (% that survived a second turn in sea: 50% (this one moved a tile))
Second: 58% (% that survived a second turn in sea: 48.2% (this one moved a tile))
Third: 44% (% that survived a second turn in sea: 54.54% (this one stayed in the same tile))
Averages: 54% for the first turn – 50.9% for the second turn
Caravel in Ocean: % of survival in turn 1 (% of survival in turn 2)
First try: 62% (% that survived a second turn in ocean: 35.5% (this one moved a tile))
Second: 56% (% that survived a second turn in ocean: 35.7% (this one moved a tile))
Third: 52% (% that survived a second turn in ocean: 50% (this one stayed in the same tile))
Averages: 56.6% for the first turn – 40.4% for the second turn
-Seafaring-
Caravel in Ocean: % of survival in turn 1 (% of survival in turn 2)
First try: 72% (% that survived a second turn in ocean: 86.1% (this one moved a tile))
Second: 76% (% that survived a second turn in ocean: 78.9% (this one moved a tile))
Third: 66% (% that survived a second turn in ocean: 60.6% (this one stayed in the same tile))
Averages: 71.3% for the first turn – 75.2% for the second turn
Graphs
I only did graphs for Chieftain. They are pretty much the same if you do it for the Monarch level tests.
My Conclusion: This appears to be quite simple: there are no other factors besides if you are Seafaring or not. If you are Seafaring, it’s 75% of survival, regardless of difficulty level, terrain, ship, turns spent in water. If you are not Seafaring, it’s 50%. It might not always been exactly 50% or 75% due to the random number generator, but I would always expect it to be within 15-20%. 
Thanks Renata for posing this question in the Quick Answers thread, and I hope you all enjoy the findings. 