Try double clicking very hard. Press LMB very hard each time you click.
You've said clicking LMB very fast works sometime. That means double-click speed is not set properly but you've also said double-click speed is set properly which is confusing. Double check the, double clicking speed! In the mouse properties where you set the double click speed, adjust the slider and test double click speed in the test icon at the right. If it works with the test icon it should work anywhere.
Most games over-rides operating system's mouse settings and use their own so there is a possibility that it works in games and not in windows.
In the land of Seatle, by the fires of Microsoft, the dark lord Bill Gates forged in, secret, a master OS, to controll all PCs.
And into this OS he put his greed, his malice and his will to dominate all computer media.
One OS to rule 'em all.