After C has been charge up (ie. S1 closed for a long time). The Voltage across C is same as E, effectively you have an open circuit at C. So initially, when S2 is closed, there cannot be any current through R1 because potential difference across it is E-V_C = 0, but as C discharges through R2, V_C drops and now E-V_C >0 and so E will charge up C again via R1 (so current through R1 becomes non-zero). And so as C discharges through R2, E through R1 constantly charges C up again. I believe the net effect would be that C is just a spectator in this process.