When you say it closes, are you saying your game crashes right after it connects? If so, try verifying your game files through steam (Right click on the game in library > Properties > Installed Files > Verify integrity of game files). If that doesn't help, try deleting your cache, download, and downloads folders in your gmod installation directory (Usually C:\Program Files (x86)\Steam\steamapps\common\GarrysMod\garrysmod). One of your downloads may have corrupted and is crashing your game.
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Slick's post in Why I Get Banned For 5 Months was marked as the answer