Why did my silver border disappear

Were you playing in a different PvP mode where you didn't earn a border? (such as you earned Silver in 5v5 and were playing 3v3 Ranked TT) The borders are queue specific, so if you're in Ranked you won't have a border from another queue type.

You can find that info on the Ranked Borders section on this page; https://boards.na.leagueoflegends.com/en/c/player-support/W0aEONuP-2017-ranked-rewards-help-desk

Also, was your Border from Season 6? You only get the border from the previous season, they get replaced every season so you have to place again to earn the new rewards.