This is symptomatic of the ill-advised use of free cloud services, I'm always amazed that nobody seems to see events like this coming. Vast numbers of people are becoming increasingly enmeshed in free cloud hosting to the point where it's very difficult to backtrack and get out.
Photobucket funds the service through ads: if readers can see your photos directly on a third party site, they never visit the Photobucket site - no ad revenue. I'm surprised it lasted this long. All other sites with a similar model are under the same pressure - Dropbox recently dropped the Public Folder facility that many people relied on, and as for the many Google free services, I dread to think - if it isn't making enough money they'll pull it (they've got form).
Often the problem is not so much the amount of data you have in their cloud but the links you have posted to it. That Dropbox fiasco resulted in a huge number of links posted over years on websites and forums being instantly broken.
By far the best solution is get it all under your control by registering your own domain and getting a low-tier hosting plan with a Web provider. It's yours, it's cheap and it guarantees your links. If the provider goes bust, or if you change provider for any reason, you just migrate your data over to the new host and all your posted links remain valid.