Ryan, this issue is known about and logged as SPR DEGN8NMGF5.
The radio group output markup for each radio option as follows:
<label><input type="radio" value="Y" name="root:_id1:radioGroup1"> Yes</label>
The clicking on the label does appear to apply focus to the radio control yet however with selecting the control hence the appearance of not "sticking". Ideally the above could should be as follows which associates the label with the control.
<input type="radio" value="Y" id="radio" name="root:_id1:radioGroup1">
<label for="radio">Yes</label>
You can achieve the same effect if the ExtLib is available to you using the Dojo controls like so.
<xp:panel id="PartialPanel">
<xe:djRadioButton id="djRadioButton1" value="#{sessionScope.djButton2}"
groupName="val" selectedValue="Y" label="Yes">
<xp:eventHandler event="onclick" submit="true"
refreshMode="partial" refreshId="PartialPanel"/>
</xe:djRadioButton>
<xe:djRadioButton id="djRadioButton2" value="#{sessionScope.djButton2}"
groupName="val" selectedValue="N" label="No">
<xp:eventHandler event="onclick" submit="true"
refreshMode="partial" refreshId="PartialPanel"/>
</xe:djRadioButton>
</xp:panel>