This song popped into my head and seems so familiar. I have tried searching and can't find it.
It's mid 60's Rock, the singer is male and sounds somewhat like the lead singer of The Guess Who in the song "Shakin' All Over", but I think I have listened to all their obscure songs and it isn't any of them. He has a little bit of a gravely voice. It's not a higher key harmony type of group like The Zombies.
The lyrics I remember (I think it's the chorus) are:
When the rain is falling <or coming?> down
blah blah blah blah all through the night