If the encounter was hard and meaningful, that counts as two out of the standard 4 required to regain dailies.we shouldn't let the rules become more important than the story. If you rest after 3 encounters and travel, sleep etc, you should take back your dailies. Actually, you could even rest after only 1 encounter and take back your dailies, if the battle was hard and meaningful.
I am a 4e and not a 13th Age GM, but the two systems are pretty similar in their rationing and recovery rules. Regulating full heal-ups and recoveries is a key part of making the "story" work in these games - otherwise players just blitz everything with their dailies.What's important IMO is always the story, something that feels right should always be possible, even when it's against the rules
Within the fiction, the reason for a lack of recovery can be narrated however the GM likes, as long as it generates the requisite sense of ongoing tension.