Why is my unit not able to pick up power in Blitz?

In Blitz, you play unit cards to spawn units, which requires power. To get more power, you can collect it by destroying caches of it around the map and picking it up.

I spawned a unit (in this case, a Jackrabbit) next to one of these caches where it then aided in destroying it (I had a Scorpion tank farther away also damaging the cache). But it wasn't able to pick up the power with my Jackrabbit for some time. Why?