Some old customers can't log in with some browsers to customer account of magento 1.9.4

Question

We have strange problem in our magento 1.9.4 web-site. Some customers cant log in to their customer account but most can. Seems that in some cases clearing browser cache helped but some customers said that it does not.

Most customer that had this problem used Chrome, but not all.

All customers that had this problem can log in to another browser they newer used to visit our site.

So seems like cache problem but it is very difficult to repair since we haven’t been able to reproduce it at our site. We have tested with macos / win / iphone / android and all the browsers without any problem.

Any idea how to solve this? We have cleared all magento caches many times and re-index etc. Seems not to help at all. Our cache settings: Cookie Lifetime 86400 Cookie Path / Cookie Domain .ourdomain.com Use HTTP Only YES Cookie Restriction Mode NO

Most strange thing is that we haven’t change anything before this problems started.

Many thanks!