To reproduce, inspect any element. In the markup view, give the element an empty style attribute, reading style="" Now put the cursor between the quotes and type something like "co". It should offer completions like "color", but it does not. If you remove the trailing quote before beginning, the completions will be offered.
Julian, I have a feeling you may have filed a dupe of this. Could you verify please? Also, I'm going to triage this as a P3, feel free to adjust as a P2 if you feel like this is a more pressing issue.
Yes, it was bug 1254070. I will close this one, since the other has a patch attached already. The other bug is marked as P2, but feel free to downgrade.