Has the website domain changed? A share is tied to a specific URL. If the website address is different, then yes, the count will be different.
I know this is Google+, but generally for Facebook, we suggest trying to set the og:url tag to the old address, so that the shares will have the old count, but the page will still get directed to the new address. Any likes would go to the old address though and not the new URL. This is a suggestion for FB, and I'm not sure that it would even apply to the Google+ network. Beyond this suggestion, if the URL is different, then there's not really anything we can do to maintain the old share counts.
-Melissa
after switched to the new hosting, g+ not showing count
