Hmm does look a bit like dodgy hardware to me, I am currently doing a project on the FOXGM and have never had a problem turning the modem on in software as long as I hold the port on, sleep for 1 second and then close it again. There was a note about the modem control port being defaulted to in rather than out on some firmware but that didn't seem to be the case with the default firmware that was on my FOX board when I received it and wouldn't in any case explain why it is intermittent for you.
Turning the modem on manually, I would suggest you follow the howto on the fox site to get a GPRS connection up just to confirm that the modem actually works and you can talk to it on ttyS2, I can't remember if I tried my modem before loading the fimage from the phrozen SDK or not, I think the phrozen firmware was my first step as I loaded the image already in the SDK and then later rebuilt it enabling the RTC and card reader on the GM board (coincidentally my GM board also arrived with the RTC clock battery in upside down which caused some early confusion when I couldn't get the RTC to hold the current time) Also before condemning the hardware you could try the default FOXGM images which are available from the acme site on the page for the GM board http://www.acmesystems.it/?id=3
