I wrote a blog post that deals with this a while back.
The SIM900 chip is designed to run off a LiPo battery, and therefore has built-in protections, lest it damage itself or the battery. These protections include an undervoltage warning that is emitted when the chip's power supply rail falls to 3.3V, as well as an automatic power down when the rail falls below 3.2V.
Because 3.3V is all the Tessel can supply, the GPRS module includes an external power input and a separate voltage regulator which, combined, provide the SIM900 with 3.465 V. It is recommend that external power be used if possible.
When the GPRS module transmits, it uses a lot of power, so much so that it may turn itself off because it thinks its "battery" is critically low. Again, lots more about that in the blog post.
All that said, it's been a while since we've seen the module power down during our own internal testing/work. Do you have anything else plugged into the Tessel?