You won't lose your 401k, it's yours. You can ask for a rollover into a new plan/account or a distribution any time after you are no longer an employee.

If the 401(k0 issues a check to you, you have 60 days to get it into a retirement account (either another 401(k) or an IRA). You would also want to make up the part that was withheld for taxes, else that portion will be counted as a distribution to you.

You shouldn't lose the vested portions of a 401(k) just because your company was bought out.

You should be able to leave the funds in the 401k that you have regardless of the company change, you may not be able to continue funding the 401k but you won't lose it. If you do want to roll it over though you have a few options, you can roll it into the new companies 401k if they offer one, you can rollover into an IRA through a brokerage firm, or you can rollover into a mutual fund IRA company. No matter which you decide you want to be sure to do a direct rollover. This will allow you to transfer the funds without a withdrawal.

I think you may be thinking of the time frame if there is a withdrawal. If you take a withdrawal and not do a direct rollover it will be considered a premature withdrawal if you are under 59 and 1/2 years of age. A premature withdrawal is subject to taxes and a 10% penalty. The time frame comes into play when you receive the money from your original 401k. In this case you have 60 days to deposit the money into an IRA in order to avoid the taxes and penalties. The problem with doing it this way and not as a direct rollover is that the original 401k is subject to a 20% federal income tax withholding and you will need to make that up when you put the remainder in the IRA or you will still have to pay the penalty on the difference from the original full 401 and the reduced amount you put in the IRA, which is calculated when you do your annual income taxes. To avoid that whole mess either leave it where it is or do a direct rollover!