Is this a recent development? Did it happen after an upgrade by any chance?

What theme are you using? Have you tried switching to a standard theme like Twenty Sixteen and trying the search then?

Which makes me wonder if it is something localized to you, but not necessarily your WP install…

What browser are you using? Have you tried any other browsers?

Are you by any chance on a WordPress multi-site?

Is there anything special about your hosting servers that you know of?

An unexpected error occurred. Something may be wrong with www.remarpro.com or this server’s configuration. If you continue to have problems, please try the support forums.

I maintain a lot of sites, and have only seen this problem happening in the past 48 hours on sites I update and then attempt to extend.

Exactly the same thing happening here.
On the ‘Plugins->Add New’ page the Featured, Popular, Recommended, and Favourites tabs all show content, but if I try to search for something, even the exact name of a known plugin, I get the ‘working’ icon for a while then “An unexpected error occurred. Something may be wrong with www.remarpro.com or this server’s configuration. If you continue to have problems, please try the support forums”

Having the same issue minus the “Unexpected Error” message. Mine continues searching for 5+ minutes, no matter what I search. I just migrated from WAMP to an online host server, and that seems to be when it started.

When icon is spinning click F5 once and refresh page. This way I forced searched terms to show as plugin list.