iMac regularly not detecting mouse/ keyboard on startup

An occasional nuisance that has always existed with my iMac is that every-so-often, I'll start it up in the usual way and find that the password I'm typing is not appearing in the login screen. The iMac screen will then go off again after about 30 seconds as if there's no use, and then I will usually have to repeat this process two to five times before suddenly, with no warning the iMac recognises both items and I am able to login and carry on with no problems.

It's worth mentioning that when recognised/ under normal conditions the connection with the keyboard and mouse are completely fine - they almost never drop out of signal when logged in (and if they do it is only for a second). Similarly, because it is always BOTH devices that the iMac does not detect I am assuming it is an issue with the iMac rather than the devices. Turning the devices on and off again during these freeze-outs makes no difference to the iMac detecting them.

I couldn't really say how often this used to happen (maybe once a month or a bit less?) but it has happened for about the third time in as many weeks lately and is really becoming something I cannot tolerate any longer.

If anyone could help with this long-standing nuisance I'd be very grateful!!