Relation Entity Collector block not working with Entity Cache

The issue is that Entity Collector cannot pick any entities after the page is cached in Entity Cache.
A perfect description of this behaviour is at #1402860-37: Panelizer is incompatible with moderation

I traced the issue down to the fact that when using Entity Cache, hook_entity_load() functions are only called when the entity is first loaded/cached. On subsequent loads from the cache, hook_entity_load() is not called, which is the expected behavior of Entity Cache as far as I can tell. Entity Cache does provide a hook, hook_entitycache_load() / hook_entitycache_TYPE_load() which lets you hook into and alter the entities that are loaded by Entity Cache (whether they are loaded from the DB or from the cache).