See the circuit in the picture...
The main GPS module (top right) sends 3.3V (3.287V measured) out of VccRF and that is fed back into V_Ant via a 10

resistor (R2). The 3.3V from VccRF also goes across a potential divider (R9+R10) which feeds a voltage of approx 3.1 V to the + input of U1.1, the LMV321 Op Amp.
If the antenna is connected it pulls approx 25 mA and there's a voltage drop across R2 and I measure 3.057 V on the - input of U1.1. If the antenna is disconnected, there's no voltage drop across R2 and I measure 3.287 V on the - input of U1.1.
Here's the problem; the output of U1.1 (pin 4) stays at 60 mV all the time (it does so on 2 PCBs I have made and tested) but my logic says that, because the - input of the Op Amp changes from above to below the voltage on the + input, I should see the output swing from rail to rail.
Is there something wrong with my understanding on how this should work? I adapted the circuit from fig 14 of the Ublox MAX-8/MAX-M8 Hardware Integration Manual where they use a LT6000 Op Amp and R2 is 560

. I have tried a 560

resistor but it doesn't change the behavior. Is the LT6000 a way better Op Amp or can you guys suggest an alternative if the issue is my cheap Op Amp selection?
Thanks in advance.
[EDIT1] I think it's because the LMV321 only works for input voltages up to Vcc - 1V while the LT6000 allows inputs all the way up to Vcc, if there's alternatives, I need a device in the SC-70-5 package.