Yes, buy the rebuild kit that is easy to find online. I have rebuilt 3 sets of mine and no problems now. Im very familiar with the R2Cs and how they work. Based on your the OP's issue description, I'd bet the 2 pawls are slipping on the lever ratchet side mechanism. In short each shifter has 2 sides, a lever ratchet side, and a cable pull detent side. The lever side engages first, and then it leads to engaging the cable pull detent side.
There are very detailed instructions with pics put out by Zipp online that show how to rebuild them.
Happy to help out if needed.

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Team Zoot-Texas, and Pickle Juice