"Thanks to you, I am successful."
Translation:Díky tobě jsem úspěšný.
wow... I have to say I needed to think about this for a while :D. I am not a linguist, but I feel the main reason is that you're not actually saying "thank you" here, which would be translated as "děkuji ti", but rather "thanks TO you" ... the "tobě" actually represents this "to you" and the fact that díky is not actually a verb, but rather a preposition (like "because of you/thanks to you"). Hope this helped and is not too far from an official liguistic explanation :).
In the present context, both “diky” and “thanks to” are prepositional expressions (think of replacing them by “kvůli”/“because of”). “Děkují” (děkuju), on the other hand, means “I thank,” which is not a prepositional expression and does not fit into the grammar of the sentence.