Circling back around to this as it is consistently happening to me, and at random. I found another blogger
here with this issue and his tip to fix. I have investigated further and it appears the image links are all pointing to some sort of a subdomain and start with some variation of x.bp.blogspot.com, where x is a number. I just made a new post on sunday night and this morning the images were not appearing. I changed the 3 in 3.bp.blogspot.com to a 2 and it showed up. I then also confirmed the other bloggers tip of entering lh5.googleusercontent.com instead. All of these seem to work. It appears to me that there is just a very high level of unreliability on these (duplicate) servers of google.
This is really making me want to switch to a wordpress site hosted on my own web server. I have been avoiding it cause I didn't want to have to recode a new site (time constraints) but the pictures are a pretty big part of our blogging and this unreliability is getting on my nerves. Hope this tip helps anyone out there!