Some players are having issues connecting to the Glyph Client, especially since RIFT 3.5 Hotfix #2.
Trion is aware of the issue and actively investigating to resolve it.
In the mean-time, a temporary, potential workaround is to exit Glyph, delete your Glyph cache file and re-launch the Glyph Client.
Your Glyph cache file is usually located at C:\Users\[YOUR USER NAME]\AppData\Local\Glyph\Cache.
For players who open the game through Steam, your Glyph cache file will be located at:
C:\Program Files (x86)\Steam\steamapps\common\RIFT\GlyphClient.cfg
You will likely be able to get more updates about the status of the Glyph connectivity issues from CM Ocho’s thread here.