Welcome to the forum!
I'm just testing this now, since this is the first time I've heard about it. For me, with 0.92.3 on Windows 7, if I press the Space bar as you explained, then as long as the Measurement tool is enabled, pressing Space toggles it. So one press shows the measure lines and text, and the next press hides it, next press shows it, next hides it. But after I switch tools, it no longer works.
Actually this is the first time I've heard about such a feature that will display the measure lines and text after switching tools. Hhm, since the manual is a bit outdated, I'll have to consult Xav's series of tutorials..... Ok, this is the best....well, it's really the only in structional materials that I know about, for the Measurement tool, in it's current state:
http://dl.fullcirclemagazine.org/issue121_en.pdf (skip to the Inkscape chapter).
I did not read it closely, but just skimming, it reveals something which I think should work for you. It's hard to describe the button, but it's towards to the right end of the control bar, and the tool tip says "Convert to item". What it does is change the measure lines and text into actual vector elements on the canvas, in a group. So they will remain there until you delete them.
I did not see any mention of a feature with the space bar, but again, I really was mostly skimming.
But finally, could I ask what's happening on your canvas, where you need the measurements to stick around on the canvas, when you switch tools? I'm thinking there's a good chance there's another way to achieve your goal. If you'd like to share your SVG file that would make it even easier - both to understand the situation and circumstances, as well as to explain a different solution. (The Measurement tool is still relatively new, and to be honest, a bit buggy, and perhaps not as polished or solid functioning tool as it hopefully will be someday.)
