Since CSS Hero does not physically modify any Theme file, but works “behind the scenes” adding it’s own separate CSS file, upgrading your Theme does not kill your CSS Hero edits, this means minor theme upgrades in 99% of cases are totally fine.
So it is a good idea to upgrade your theme for example from version 1.0 to 1.1 [or from v 2.2 to v2.3] and expect things to keep on working the way they were.
A different expectation is when a major theme update is done – Eg from version 2.4 to version 3.0.
In these cases, if you upgrade your theme, you might experience some loss of your customizations: if the Theme author has radically changed the Theme structure and/or some class names, the edits you’ve been doing with CSS Hero may not apply anymore.
The bottom line
Before planning any major theme update, a good idea is to backup your entire site. You might experience some problems, and if you don’t have a good understanding of things, fixing them might be a pain.
Minor theme upgrades are generally safe, and it is a good idea to do them, mostly for security reasons.