The clearance comes with the catch that you need to maintain the minimum visibility requirements and sky conditions, if you're not able to, you have no clearance, it's pretty much as simple as that. Either you need to navigate in such a way that you avoid the weather (which might require you to leave the airspace) or you can do one of two things
- Request an IFR clearance if you're rated and equipped
- Declare an emergency and land in the nearest suitable spot, assuming you can still see the ground
If it is deteriorating so quickly that you cannot go back to where you came from (i.e. the weather is not better outside the D), you'd be flying illegally outside the D as well, so no point in going there really, but more importantly, if the weather is deteriorating that dramatically, you don't have much time before you'll be completely blind, and by that time you'll want to be on the ground with as little injuries as possible, no matter where or the condition of the aircraft.
Note that the minimums are different depending on where you are (jurisdiction) and type of aircraft.