You have not given us any computer details or specifics - can you please add this information, as it is really helpful in trying to work out where the trouble lies. Basic stuff such as:
OS, OS version, Computer specs, installed memory, hard drive configuration, available space on hard drive, graphiocs card etc - the more info you can give the more likely someone will be able to spot the problem.
It also helps if you can list what things you have already tried, along with the results (even if a fail, how did it fail etc) which will save others from suggesting things already tried.
Honestly, I am not nagging here - this is essential information on so many levels.
Other massively helpful information is your project details - as many as possible, including sequence count, run time, how many tracks are being used for both audio & video, how many effects and/or transitions are in use but not yet rendered, what your project export settings are, and perhaps even more important what your assets are and their specifications - for example, if you are running several nested tracks of full HD at 60fps this will hit your hardware considerably harder than one or two SD sequences will. Seriously - the more information you can supply the better, please.
To attempt an answer for you right now is impossible as we don't have enough info.
Have you tried clearing your media cache? You may be surprised at how often this helps out.
Also - and this is a nit pick but an important one - you are not trying to move an 'audio slider' (which implies a fader in the Audio Mixer) you are trying to edit an automation point.
I think at the point you are describing if clearing your media cache does not help, or setting the cache files to be alongside the main assets fails (this prevents the CPU having to swap across drives if your cache files are on a different HDD) then I would do a full uninstall/reinstall of Premiere. This is an option of last resort though, and I feel (in the face of almost no information) that the issue could ever so easily be running out of resources
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