I quite understand why thymine is present in DNA. So we can mark it out where cytosine undergoes a reaction and is converted to uracil. Then we can repair the DNA.
But how can we make that out in RNA ??
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RNA is shortlived and need not undergo repair. A "mutated" RNA will degrade and will be replaced by the correct RNA.
Even though RNAs are shortlived compared to DNA (which does not really undergo turnover), some RNAs are stable and have low turnover. Nonetheless RNA would be present in multiple copies it is improbable that all of them would have undergone mutation.
Moreover RNA with certain mutated codons e.g. non-sense mutations are cleared off by the exosome.
Thanks to har-wradim for pointing out about RNA repair mechanisms. There are few reports that say that methylations in the RNA can be corrected by the enzymes AlkB (in E.coli) and its eukaryotic homologue hABH3. These enzymes were known to repair methyl lesions in the DNA (1-methyladenine and 3-methylcytosine), but it was subsequently shown that they can act on RNA as well [1,2].
However there seems to be no mechanism for repairing deamination damage; this study has demonstrated an artificially designed system which is capable of targeted RNA deamination (but there is no system yet that can fix a deaminated base in RNA).
This article comments that AlkB is tightly regulated because if uncontrolled it can demethylate functional methylations too. Overexpression of AlkB is actually toxic to the cells unless they are under alkylation stress by agents such as EMS/MMS (Ethyl/Methyl MethaneSulphonate).
But IMO RNA repair is not as essential as DNA repair because of aforementioned reasons.