Drivers seat belt won't retract

AS seat belt operation is paramount safety it would be in you best intereste to have the unit replaced as something is faulty in the setting and retention area.

Get a new one or a use one and repalce it your self

2005 Towncar SRS Code 33 (3 flash + 3 flash, repeat this set for twice. then Beep 5 times pause x 5 = 25 beeps every 30min).

This means you have problem with left (Driver) side pretentioner (Seat belt retract system).
It doesn't mean physical belt or retract mechanism.It is just bomb wiring which is part of airbag system.
When airbag deploy, passenger must stay tight in seat otherwise body lean to front then slam back to seat by airbag.
if belt is loose or delay to lock, passenger's body rocks back and forth.So, system use small bomb (Fire power) to lock and retract seat belt when airbag deploy.There is small bomb and igniter in part of Seat belt retractor.
Code 33 is warning for this part on 2005 Towncar.(older model is different meaning in Ford/Lincoln, it's possibly passenger side airbag system for earlier model)
Before you work for any part of Airbag system and touch any "Yellow connector", * *Disconnect battery (negative side is good enough) and wait at least 5 min to clear all power in system**.(Airbag store back up power for few minutes to be able to deploy even in case if power disconnected)
by the way, you should move your driver seat most forwarded position before you disconnect battery to make it easy to work with seat belt.
locate driver side seat belt retractor (in center pillar between front and rear door, you may have to fight with weather strip)

Locate Yellow connector on bottom of Seat belt retractor (it's called "Pretensioner")it is located on very bottom of rear side of retractor.
only one yellow connector. (make sure your battery is disconnected)
Check its physical connection or looseness.if connection looks fine, you may have to replace whole seat belt ($180-$200 in Lincoln dealer)
You can check if pretensionor is good or bad by regular tester, but unless you know how, I won't tell (because I don't wan't you to blow out pretentionor).

possibly there is something stuck in the belt not letting it retract

Are you trying to say the seat belt retractor is stuck? This is in the front seat?
If it's anything like my Tahoe, you need to remove the plastic panel that covers the retractor (carefully - don't break the clips or you won't be able to put it back on). Take a large flat head screwdriver and slide it under the part where the seat belt coils up, and find a little tab - push it with the screwdriver. As long as the seat belt is not twisted up, it should retract.

have a look to see if its coiled in twisted as you pull the belt out if the buckle doesn't line straight to the female end well its probely retracted in twisted to repair pull the belt out all the way and then realign the belt its quite hard to do so take your time hope this helps.

Try pulling on it VERY SLOWLY if that don't work then you need a new belt.

Check Honda for recall. Remove fuse, manally retract & use seat belt manually. JUST make sure you are using the seat belt!

Try giving it a solid tap with something hard (screw driver handle) while jiggling the seatbelt.

1)move the plastic cover over the seat belt out of the way to gain access to the two mounting bolts for the seat belt mechanism. Use a 10mm wrench and a 14mm wrench and remove the two bolts holding the seat belt mechanism to the body. Use a small drill bit or small screwdriver and make one hole in the plastic cover on each side of the seat belt mechanism (the covers say "do not remove plastic cover". Spray lots of wd40 in each hole. Then exercise the seat belt. When the mechanism allows the belt to be retracted, retract the belt all the way out and exercise the seat belt. Reinstall mechanism with both mounting screws in original position and put plastic cover back in place. Good luck. New seat belt costs $100.00 from dealer and are hard to find working in junk yards. I have fixed several of them this way.