One of the other challenges with low frequency combat is that with so many combat abilities, if you only run one combat a day or week, players are going to turn it into a cake-walk.
How would you resolve this? Use higher CR enemies just less often? Is there anything else you can do to make those single day fights more affecting?
Yes, this is a problem. A CR-appropriate challenge is no challenge when the players know the can nova and rest. Some tricks I have used to restore challenge (I don't claim it's even approaching the original challenge level, but it made fight more interesting and less a cakewalk).
1. Use monster with several phases. Useful for bosses. So when the regular owlbear is killed, easily because, hey, nova'ed from everyone in the party, in its place stands... an Enraged Owlbear. With a whole new set of HP, improved stats and free of any previous detrimental effect put on it by the team (I don't say it's a transformation, but I usually signal that the opponent is bloodied and enraged, so when this means its a transition, I also mention a renewed will to fight in the creature's eyes). This has been used in published monsters (Auril in RotFM but I am sure there were a precedents). I have been doing that for a long time. So, players will often want to save their more powerful powers for last, when it's not "overkill" to do that. If the opponent was single tiered, they saved their most powerful powers for naught giving the baddie time to inflict actual damage. For bosses, their whole design can change (a party once fought a spirit of war, it first form was a brutish warrior, his second form was a general (the players loved when he ordered the trees to attack the characters... the characters themselves didn't like it as much when the trees complied) and his third form as a deceptive and cunning warrior who thought victory was more important than fairness. Giving at each stage theme-appropriate powers made the fight memorable and three Hard encounters in a row were worth 5 to 7 average encounters... When the boss fell, the players were genuinely relieved and hoped there was no fourth form, the Samurai, modeled after a wuxia hero (I had statted it but as I was not sure of the overall difficulty I decided to have this form only appearing if the first three were defeated too quickly for the fight to be challenging).
2. Add mooks. The fight with O-ren Ishii was what mattered, but the crazy 88 were fun, too. Have many opponents with 1 HP so characters can (and should) waste area effect powers on them. With bounded accuracy, 88 mook can wreak havoc on a party if left unchecked. Have the players know that they are mook so they don't flee... And if they are on the same page, they will like having fighters cleave a trio of kobold with a single attack (yes, you can stat three mooks as a single opponent... not everyone is entitled to an attack every six second after all) and it will make the villain all the more competent by contrast when the PCs reaches him.
3. Add environmental hazard to make fight more difficult. Fight the water spirit? Cool. While having water half-waist? Less cool. While the temperature is going from freezing to scalding the more his blood seeps from wounds into the water? Challenging.
4. The most difficult: use higher CR creatures. I rank it last because the CR scale isn't linear. A higher CR creature can have damage that will one-shot players of a low level, or have access earlier to strategy the players can't counter.
Expect your fights to last longer, as there will be fewer of them it leaves ample time for other activities.