A few more off the wall possibilities.
The dive of the cliff.
1- Karr dove over the cliff and perhaps activated something heavy to explode so when he hit the water he would not completely sink. It might not have been enough to remain drivable, but least he would be floating back to shore.
2 - Someone saw Karr go over, and pulled him out of the water later. Karr was fine, but flooded, and it took 2 years for enough sand to build up around him to help his engine and circuits dry off enough that he could come back online. It's possible whomever pulled him out, may have had the means to pull him out via some machine, but didn't have a way to tow him out of there, so after he/she/they pulled Karr out of the water, left him on the sand and went to find something to tow Karr away with and never made it back due to some reason... death...road accident... or maybe something Karr did scared them off for good?
1. Perhaps Karr did sink to the bottom. But the tide of that beach only goes out for certain amounts of time of the year? Karr may have dried out enough to come back online, but was stuck under too much sand... eventually the sand was washed off enough for Karr to be found the next time the beach dried up enough and Karr was able to come back online from being unburied when he was.
2. Early nanobot technology? It was something Bonny was not aware that others tested on Karr, but they where not fast acting like in 2008... they took some time to rebuild Karr due to sand and water damages, but eventually got there enough after 2 years?
5. Garth knew of the event, and began repairs to Karr... he needed to steal something from the FLAG to get Karr up and running again, but whilst away, someone else found Karr and got him going. Maybe Garth thought the problem was not fixable due to the voice box not working? There are endless possibilities regarding that.
6. Kitt deactivated Karr on the way down, then got bored one day and reactivated him and lied to Michael and FLAG because he just wanted to have a worthy opponent for a few days.
7. The Karr of the future (2008) sent a Terminator back in time to fix his predecessor to try and stop something or other... and perhaps succeeded? As in the 2008 series, KARR is still a prick, but no one had learned their lesson from building the original KARR that went bad?
8. The A-Team heard of the incident, Mr T pulled Karr out of the water all by himself. The team fixed him enough to get him to the state he is found in, but couldn't get something electrical to work, so they sought out MacGyver to help them fix Karr with a bobby pin, rubber band and stick of gum... but MacGyver wasn't found in time, and the others found Karr whilst away.
9. Doc Brown and Marty stepped on an ant in the year 19,1955 B.C and it caused a ripple effect in the time line continuum that resulted in a shift in the Earths atmosphere causing ShowNash Cliff to become Clayton Beach instead of Eastwood Baywatch Reserve... also restoring Karr to perfect working order.
10. Karr had time travel abilities, but could only be activated while doing 120 mph in a nose dive... he traveled to the year 2012, saw Jersey Shore and tuned into a Justin Bieber song and decided the future sucked, so he went back to his own time and crashed into the sand and couldn't get out, so he hybernated till he was dug out.
11. April was ticked off that FLAG rehired Bonnie and told her to leave without a trace, so she went rouge and restored Karr, but left him on the beach to be found so she would not be suspected of any blame?
12. A young Mitch Buchanan gave Karr CPR after he saw him fall off a cliff. Mitch called it at 17:55, and walked away, figuring it was a car, it didn't need to be buried, but in fact he actually did save Karr, it's just cars don't breath, so Mitch was a dummy. He left Karr there and Karr was in a cybernetic coma for 2 years.
13. It wasn't Karr at all, it was a Deceptacon that scanned Karr and copied him.