Log-in on iphone or tablet works with one site but not with another

I help maintain one WordPress website and have developed another from scratch.

I can log in to the former site (tennisclub) on iphone, ipad or Windows laptop.
I can log in to the latter (mikas) only on Windows laptop. I think I used to be able to log in to this on iphone and ipad, although my memory may be deceiving me.

Can you suggest anything that may help solve this problem?

Thanks,

Mike