What does the valediction "Ever yours" mean?

Solution 1:

"Ever yours", "Yours ever, "Yours Always", are used less today at least in the US and usually imply some persistent affection or friendship, but not necessarily a romantic connection.

Webster Online says it's just a way to end an informal letter

A book entitled Ever Yours: The Essential Letters contains letters from Vincent van Gogh (1853-1890) to various people he knew.