Ubuntu should be able to. They even have some sort of kernel hot patching service I have not used.
If you do not care about kernal updates then most distros should be fine. Just ignore the reboot suggestions.
Edit: If you do not reboot you might want to make sure critical things are restarted such as you web browser. Or just logout and login again. One hopes the distro appropriately handles service updates but who knows for certain.
Low blood pressure can cause this too especially if your on meds that can lower blood pressure. For me a cup of coffee, working out in the morning, and being careful when I take those meds helps.