Can TPS3700 undervoltage overvoltage monitoring IC drive relay directly?
The 40mA is an absolute maximum spec and not a place where the device is intended to operate.  Even 20mA is a stretch, and TI doesn't specify what voltage you will have across the drain-source of the internal FET at that level.  You can see the operating specs specify the output voltage at currents in the range of .4 to 5mA.

These devices are not intended to drive relays directly.  It's very simple to use a 2N7000 type FET or a 2N3904 BJT hooked to the supervisor part to drive the coil.  Always use a diode across the coil to prevent the inductive kick during turn-off from killing your switch device.  (The diode should be rated for something like 1.5X the coil current, and for a voltage greater than the coil supply voltage.)

There's a nice diagram of a relay driver in the first post here: http://forum.allaboutcircuits.com/showthread.php?t=29461 

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