I have been looking around for solutions to see if there is anything I could gather. From information I've seen this is what I could gather for possible fixes:
Change your password
After changing it, double check to ensure you are typing it in correctly.
Try clearing the Jagex Cache files
Bonus Point: This helps to make things harder for Jagex to link your accounts together and decrease bot bans.
Uninstall the launcher and OSRS launcher (if applicable)
Reinstall and it should work off the bat. Try #4 if #3 doesn't work.
Use an OSRS cleaner tool after uninstalling launcher and OSRS and do complete removal.
*Reports of having accounts locked after using this because it thinks its a brand new computer -As in you have to unlock, email verification, and change password.*
Here is a link I found to a Random.dat deletion tool - Scroll to the very bottom to "Random.dat File(s):"
The program may do a Quick Removal, which is designed to be ran once in a while to keep your Random.dat file fresh, while the Complete Removal is designed to completely wipe-out all of the files stored on your computer associated with Jagex. It is recommended to run this mode after a ban. Also, when running the Complete Removal, you will need to re-install the cache files by running the official game client.