erode
ih-ROHDverbMeaning to wear away slowly
Memory hook e-RODE: gnawed away, as by a RODent. Night after night, a little mouse nibbles the big wheel of cheese until only a sliver is left. Rodere means to gnaw: water, wind and time erode things the same slow way.
Waves eroded the cliff a little more each winter.
In context Small broken promises eroded the team’s trust in its captain: no single one mattered much, but together they wore it away.
Similar wear away, wear down, corrode, undermine
Opposite build up, strengthen
From Latin erodere, “to gnaw away”: e (away) + rodere (to gnaw), the root of rodent.