To set a field to null, you must explicitly mark it as being "nil". An example of the syntax is below. In this scenario, the "MiddleName" field is being set to null:

<MiddleName nil="true" />

The other thing to check is the number of fields you are setting to null per constituent in one call. There is a limit of 10 fields being set to null per constituent per call. This is done intentionally to prevent unrecoverable disaster should too many fields be sent as null. If you need to null out more than 10 fields for a constituent, break the update into multiple requests with each request containing fewer than 10 nulled fields.