Why is the Dissolve Tool not working?

Assuming you are getting the "Invalid Topology" error you need to make sure that all geometry in this feature class is correct. Make sure the layer is in a File Geodatabase Feature Class format. Run the "Repair Geometry" then try DISSOLVE again.

Dissolve can create VERY large features from a large amount of small features and it can be a very memory intensive operation and thus take a very long time depending on the complexity of the input feature class and the dissolve parameters.

There are also other considerations when running dissolve explained in detail in the Dissolve Help and the How Dissolve Works.

When you feel that you have complied with all the usage requirements for the dissolve operation as outlined in the Help Usage article, you can submit a request for Support Assistance with ESRI. They have been very quick to respond lately. (within 24 hours) They will run the same steps on their end and provide you with solutions. You will need your ESRI customer number to request support.

Try copying it to an FGDB and run the tool. Maybe there are better chances when you run in an FGDB. Better Luck.