I currently have my dishwasher installed in my kitchen. I ran the plumbing from a hot water branch located from my basement. Since the dishwasher is not near (or even on the same wall) as my sink I had to run the drainage line to my basement sink which is located directly below the dishwasher (about 8 or 9 feet below). I have looped the drain line at the dishwasher and then ran it through the floor to the sink where it ties in on the verticle before the ptrap. I have noticed that the dishes do not get clean all the time and now the dishwasher will remain locked in a cycle. The repair man said that it could be due to syphoning of the water. How could I resolve this issue?

Repair man wrong, don't call him again. So you are using a loop for your trap, how small of a circle did you make this loop? What do you mean by locked in a cycle?

I don't know Bob, I think I might disagree. If dgsmiths set up is like this drawing, the drain plumbing would probably cause a siphoning action. If the siphoning from the wash cycle is still going on when the rinse cycle starts, it would pull all (or some) of the rinse water out.

I think I agree with Harold on this.
This is the very first time I've ever recommended installing a counter top air gap instead of a high loop but this installation needs a physical gap in the drain to prevent any siphon action from happening.
A counter top air gap,(see image) would solve the siphon problem.

Without a drawing or something from dg I can't figure this any better. However, a drain line lopped and then dropping 9' to another level to a sink doesn't have much of a chance to siphon back into the washer, in my thinking. If anything the loop trap would get siphoned and we'd be hearing about a sewer smell. How about dg, can you answer my question in post #2 and maybe attach a drawing?

The drawing above is close, instead of the vent pipe it is entering in the sink cabinet, and it appears that the syphoning is occurring. I have the option of placing a p-trap off my basement sink vent pipe just below my main floor about 10' away.
Where would I get an under counter air gap from? I check home depot but nothing there.