I'll toss this out there.....
Most beaches require or strongly advise you air down to about 20psi so you don't get stuck. I know a lot of people opt not to because they don't have onboard air or are afraid they'll tear up their tires after getting on the pavement before airing up.
Word of caution, as cool as the Dukes of Hazzard Charger was flying thru the air, trust me when I tell you a Jeep will not perform the same stunts should you be hitting ruts at 40mph.
Are you going thru the rut perpendicular, meaning both tires are in and out simultaneously, or are you taking them at an angle and flexing your vehicle farther than it was built for?
Sorry, but I think you'll need to be a little more specific in your description of what's happening before we can offer any help.