When should I accept that an endgame is genuinely a theoretical draw rather than keep pressing on?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws and is regression-tested against the official 110-diagram repetition casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it against the engine before publishing.
Direct answer
Once the material genuinely matches a known theoretical draw and the defence is playing accurately, accept it rather than pressing indefinitely. A lone chariot against an intact defence of two advisors and two elephants is the clearest example: no amount of further manoeuvring changes a result that the material itself already decided.
Why pressing on is not automatically wrong, but has limits
Continuing to play a known draw is completely reasonable against a weaker or fallible opponent, since real games are not played by theoretically perfect defenders. The distinction worth making is between playing on for a genuine practical chance and refusing to accept a position that is not actually going to change, which mostly wastes clock time for no real prospect.
How to tell the difference in the moment
If you have checked the material against the known table, in how to tell if an endgame is a theoretical draw, and the opponent has shown they know the correct defensive technique, further pressing rarely achieves anything beyond risking a blunder of your own. Against an opponent who seems unsure of the defence, playing on for practical chances is still perfectly reasonable.
Related questions
Is offering a draw in this position considered good etiquette?
Generally yes, and continuing to check or manoeuvre pointlessly after both sides clearly know the result is not well regarded.
Should I ever play on purely to save time on the clock for later?
That reasoning does not really apply to accepting a draw; if the position is genuinely drawn, agreeing ends the game rather than saving time within it.