They didn't really "explain" it at all, actually. It's just been very consistent behavior. When a Shifter is damaged to the extent that they bleed they will either: heal, or Shift. (or die maybe) Priority goes to Shifting, and if they opt not to Shift, they will begin to heal the damage. Eren maintains a cut on his finger so that if Pikku shot him, he could transform before the injury killed him. When Eren decided to not transform, the injury immediately began to heal. In 117, the way the Paths lightning is leaking out of Eren's wound seems to confirm this. Eren was constantly ready to transform, and because of this, he did not recover. So recovering seems to be the passive effect. While healing, a Shifter cannot transform. Eren had no access to his Shifting until his fingers healed when he tried punching Dina. It's unclear whether or not his human form can use his accessory powers even while healing, since Zeke can still Shout, and it's hard to tell if Eren's hand was fully healed when he punched Dina, because the panel before it, his fingertips are healing. There's no smoke when he makes contact, however. Levi cuts Zeke's legs off before the healing is complete, because once the healing starts, Zeke cannot stop it. No character has turned off the regen to transform; however, they can selectively heal certain parts of their body. Once the steam has cleared, they can Shift again. Shifting fuses part of the Shifter's body with the Titan, and as a result they would need to heal the damage once they come out. Same rules apply. Eren fully intended to transform again when he was scouting as Mikasa fought the Warhammer, the recovery staved off as he were in 'Shifting Mode', so he could transform when the time was right. Eren staved off the recovery of his hand when talking with Reiner so he could transform after recovering his leg.
Being unconscious forfeits the ability to transform, so stamina becomes a factor in whether you Shift or not.