JPEG is not a working format. It's a lossy format for final output. You should never be working in JPEG, as your work will look rubbish. I don't think Photoshop can even rotate JPEGs losslessly, due to the way that they are compressed in horizontal lines, with each pixel relating to the one that is linearly next to it (cannot think of better words to describe this at the moment). More complex transformations would have an even worse result.
You working files should be in a lossless format, like TIFF for portability, but it makes most sense to use .psd if you are using Photoshop.
If you are working with files that were in .jpg format to begin with, save them as .psd before you start working with them.
When you need final output, for the web, email, etc, use the Export function, where you will get fine control of the compression level, with live previews.
If you really want to work against all sense, I think you should be able to easily save as JPEG from the Save As dialogue box by wrapping your filename in quotes, with the .jpg suffix (although I cannot test right now to make sure). After the initial Save As, CTRL+S for Save will do.