[Galaxy S II Q&A, Help & Troubleshooting] PantsDownJedi:
That is correct. Just keep in mind that to ensure you avoid the superbrick bug, siyah or another kernel is best use for flashing the new ROM. Once the flashing is done and you reboot, you'lle have whatever kernel was included in the ROM.

Also, most custom ROMs have root installed but were you to flash a ROM that didn't, you would lose your root since it clears your system partition where the actual su binary for the superuser app lives and from reading the thread it seems that you most likely had either just happened to get corruption on the su binary, the superuser app that hands out permissions to which apps can use the su binary (the prompt that comes up when you use an app for the first time when rooted), or you may well have flashed a new ROM that wasn't rooted and happened to still have the superuser or supersu app still installed and showing up in the app drawer. Its unusual that developers don't include root but I've seen them do so.

As for your original problem, the easiest thing (once comfortable with the short and simple process but irregular looking recovery screen) you can put a file on your external_sd or sdcard if you don't have an external one (I always keep one on both) that will install root from the factory recovery mode (which looks much differant than the CWM recovery), or CWM in the case that you have CWM but no root. It gives you the option to install from a zip on the external_sd or sdcard (just keep a copy on each one), and then you can flash a file that will install the su binary and the superSU app. Its really useful because you never really have to worry when you lose root after this. Download the file and just put it on both your sdcard and external sd card and forget about it until you might need it later and also bookmark the link in case you need a more recent version at some point though usually a really old version will suffice and you just need to open SuperSU and update the binary and update the app in the market. Someone else mentioned it but it got passed over. Its a little daunting when you first use it because its a foreign looking restore screen (the real restore screen opposed to the alien CWM one). The link I grabbed from the previous poster, is here http://download.chainfire.eu/298/SuperSU/CWM-SuperSU-v0.99.zip though there is a thread with updated versions as they come out; I wasn't able to find it for now. As I've said though, I've installed old as dirt versions of this then just open SuperSU (differant looking icon if you've been using Superuser but essentially the same functionality and the move seems to be more toward SuperSU anyway) app and update the binary and update the app in the Play Store. Easiest way is to turn phone off, boot it by holding the power, home, and volume UP key, look at the funny looking restore screen until you have options. The restore screen may have a dead android on it when it completes loading but don't let that discourage you. Then find the selection for installing from the external sdcard and select the file linked to and reboot.

There is a much simpler and clearer tutorial for this but as I said, I didn't come up with it in my search and got frustrated the more I tried.

If you ever install adb on your computer, you are also given the option to 'sideload' the file from your computer in which case it wouldn't need to be on your phone but having on the phone is really easy, conveniant, and a life saver at times.

One last thing, as I don't recall it being in the thread, is that the siyah kernel and many other kernels, as they often built from the siyah base, has an option in the extweaks app from the play store, or stweaks if your version of siyah installed it for you, to install root on every boot. Its good to simply have this enabled. You need root to access these apps (and extweaks is depreciated for some of the newer kernels so use stweaks where its warranted and extweaks when it is) however having it set up to install root on every boot is a good idea if you aren't that confident with your skills. I can't say for sure, but it probably just looks for the binary and proper permissions and installs it if these things aren't correct (its what a programmer would do since the su binary does get updated). I was supprised no one mentioned this, though it wasn't really an option since you needed root to enable the feature before hand.