Should search engine validation meta tags be removed following validation?

All methods should be left in place for Google verification.
Removing them will unverify your site. It isn't brought up on the main verification info page, but tacked on to the end of all the detail pages for the methods(meta, HTML, DNS, GAnalytics), eg:

Don't delete the tag from the page, as this will cause your site to become unverified.

I don't know about Bing.

I contacted Bing, as I couldn't get a clear reply for Bing. This is what they replied to me:

Thank you for contacitng Bing Technical Support. This is (Name removed). Please allow me to address your issue regarding meta-tag verification. Specifically, you're asking if you should remove the meta-tag after verification. Apparently, you shouldn't remove the meta-tag. Please be reminded of the things you should note when your site has been verified: .Only verified sites can be used in Bing Webmaster Tools.

.Do not delete the verification code from your site if you want to continue using the Bing Webmaster Tools. Verification is performed every time the tools are accessed and then again approximately every 20 minutes or so during your session. Removal of the verification code will prevent Bing Webmaster Tools from verifying your site, and thus deny you access to its tools for that site.

.Bing Webmaster Tools stores the verification permissions in a cookie. Be sure cookies are enabled in your browser

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