How to update taxonomy term of a node using services
I think your JSON format to create node is wrong. Please check the created node. I guess it creates node but with empty taxonomy field. 

The correct format to create a node having taxonomy term is like follows.

Assuming that your 'widget type' for 'term reference field' is 'Select list' or 'Check boxes/radio buttons'

{
    "title": "my title",
    "type": "page",
    "field_mynodeterm": {
        "und": "3"
    }
}


here field_mynodeterm is machine name of your 'Term reference field' (which is used in content type).

Similarly you can use the same format to update the node

{
    "title": "my updated title",
    "type": "page",
    "field_mynodeterm": {
        "und": "5"
    }
}


If you use 'Autocomplete term widget (tagging)' as widget type for term reference field, the JSON format would be the following

{
    "title": "my updated title",
    "type": "page",
    "field_mynodeterm": {
        "und": "termname"
    }
}


I tested the above scenarios and working fine. Hope this helps.