The puzzle entailed in erosion of democracy by backsliding — a process in which the incumbent government takes every opportunity to reduce citizens' ability to remove it by democratic means — is how a catastrophic situation can be gradually brought about by steps against which people who would be adversely affected do not react in time. We investigate conditions which render democracy impregnable to backsliding and conditions which make it vulnerable. Democracy is sustainable, free from the threat of backsliding, when opposing politicians are neither very attractive nor very unattractive to citizens. To sustain it, citizens must allow more appealing incumbents to gain some security in office. Backsliding occurs either when citizens knowingly consent to erosion of democracy because they find the incumbent highly appealing or when citizens unconditionally oppose the incumbent, so that the incumbent can remain in office only by backsliding.