DAMN it’s happening again. I really don’t want to clear my cache again. I’m becoming suspicious that this is caused by travelling (ironically) and attempting to access sits/inbox/searches whilst logged-in at a different IP address.
So, I have a VPN with dedicated IP and will try with that enabled. 
Edit update: VPN made no difference.
This time I cleared the cookies ONLY for TrustedHousesitters.com (in Safari “Advanced” settings) and it worked, I can log-in again. Interestingly that also logged me out of this forum.
So, the reason for this issue is still a mystery and clearing Website data is the only solution I have found. It’s bound to happen again, so I’ll keep monitoring the circumstances.