You attempt to process your cube and get the error “the size specified for a binding was too small, resulting in one or more….”. Ok, ok, I get it, the screen is plagued with blotches of red and there does not appear to be any specific error codes in each of the processing groups.
It is likely one of your dimensions now has an incorrect data type due to changes in the underlying source. To resolve you may need to first refresh your data source view, check which objects are detected in the change list, then head over to the dimension that refers to that column in the data source view.
Once in dimension editor, select the attribute over in the attributes section, then in Properties, check the data type that is specified for each of the KeyColumns and NameColumn properties. Expand until you see DataSize, make this something appropriate, then save and reprocess.