After some discussion on a similar thread ( Multilevel model using >16GB of RAM ) and remembering and re-reading this blog - particularly the sigmoid example: https://www.martinmodrak.cz/2018/05/14/identifying-non-identifiability/ I think that yes there is an identifiability problem in the model. There will always be some values of day - delay that will result in this term = 0 meaning for those values k can have any value and A can have any value.
Unless there is some way to constrain (day - delay) ! = 0 ???