Kind of difficult to respond after you already received a number of conflicting answers...
First, I'd suggest you check out the types of shaft seals
there are as the type you have will dictate how tou should maintain it. The previous answers all seems to imply you have a certain type which is difficult to know without a further description. There are a number of how-to boat maintenance books available should you want to study up.
Of the various seals, some are supposed to leak, albeit slowly, and others are so-called dripless (and there are a few different types of these as well). Again, what you should do depends on what type you have. The good news is that it is apparenly leaking slowly so no worries as they seldom fail catastrophically.
Let's assume you have the older type grease filled seal and you have used the correct grease which is not water soluable. It should not leak at rest but may when turning. If this is the case, you're fine - if it is leaking at rest, there are two likely possibilities:
1. wrong grease, and
2. air pocket entrained in the grease container.
If you can be a little more specific about what you have and what grease you used, maybe we can eliminate the guessing of what might be a problem.