I am not into good cheap GSM modules, but if it has to work under low signal conditions, make sure you have a good antenna and use it properly.
Frequently the design is almost finished and then somebody says: "We need an antenna, where do we leave it, we don't have space?" Frequently the antenna is put at an inconvenient place and doesn't perform or is subjected to interference coming from some fast digital circuit. The lower band (around 900 MHz) is mostly the hardest one, as the antenna needs sufficient distance from metallic structures and/or solid dielectric structures (for example thick plastic layers). So it is not the antenna alone, but also where you place it.
When the antenna needs to be inside a housing, close to wiring, PCB, battery, etc, you will very likely make mistakes if you are not familiar with antennas. A moderate modem with good antenna will very likely perform better then a very good modem with bad antenna.