When KMnO₄ is added to oxalic acid, the decolourisation is slow in the begining but becomes instantaneous after sometime because

$2{\mathrm{MnO}}_4^{-}+5{\mathrm{C}}_2{\mathrm{O}}_4^{-2}+16{\mathrm{H}}^{+}\to 2{\mathrm{Mn}}^{+2}+10{\mathrm{CO}}_2+8{\mathrm{H}}_2\mathrm{O}$
Here, KMnO₄ is a reactant in the reaction which forms Mn²⁺ which acts as an auto-catalyst. The reaction is slow initially because MnO^4​− is getting converted to Mn²⁺ but once Mn²⁺ forms, the reaction becomes faster due to the catalytic action.