This VERY heavily depends on your state and I'm sure a lot of other factors. Years ago when I set up my single-member LLC my lawyer was quick to point out a thousand ways the LLC would be useless in court. Mingling bank accounts was only one of them.
The IRS, for what it's worth, treats a single-member LLC as a sole proprietorship and all losses/gains are considered personal income.
As always, check your state laws and consult a real, in-person lawyer.