The stock joystick configuration file is bad. Releasing the MFD button turns the RWR off. It's easy to fix. Open your joystick config file World 2.5\Mods\aircraft\F-5E\Input\F-5E\joystick\default.lua in a text editor and search for RWR Indicator Control POWER Button ON. Remove the value_up part like so:
{ down = ic_commands.Power, up = ic_commands.Power, cockpit_device_id = devices.RWR_IC, value_down = 1.0, name = _('RWR Indicator Control POWER Button ON'), category = {_('Instrument Panel'), _('RWR')}},
Backup the original file before changing anything. Remember that the file is overwritten with DCS updates, so it's best to use a mod manager.
Cheers