Hi Karenmarmstrong.
Welcome to our Mattress Forum! 
I am sorry to hear you have issues with your new mattress.
Latex in general is the most durable foam material in the industry so outside of any defects in the latex itself (which is very uncommon) if there is any sagging it would be in the quilting layers or the base layer under the mattress or in many cases what they are calling “sagging” is really what I call “virtual impressions” which are the result of choosing a comfort level that is too soft. You can see some more detailed comments about this inpost #2 here
I’m guessing what you’re experiencing would be a the initial loss of “false firmness” of the mattress, as even very low density polyfoam won’t lose structure in one month. Depending on what you have as a cover you could also be experiencing settling of the fiber material, as well as some settling if the top quilt panel was cut a bit too large.
The first thing I would check is to make sure that your support system is still perfectly flat and that there are no parts that are sagging or that are bending under the weight of the mattress and the people sleeping on it. It should provide similar support to having your mattress on the floor and you can test this by putting your mattress on the floor to see if it makes any difference. If it does then it’s possible that your support system could be part of the problem as well.
You did not include information about your system or all the foam layers and components that are used within your mattress including the covering but generally speaking there is always a gradual softening and the breaking in of the materials when a product is brand new. I do not have the mattresses in front of me so I can’t tell if what you are experiencing is the normal break in or not but it would be extremely unusual for latex to develop any deep body impressions within such a short period of time. Up to one and a half inch impression is considered an industry standard however it would be very unlikely that this would develop within the first month. Some brands with all latex beds have a tighter tolerance of 1" or so, but this varies by manufacturer.
Latex in general is the most durable of all the foam materials and generally holds up very well for a very long period of time but there are several possibilities that can account for your experience that are listed in post #4 here.
The material I provided can help identify if what you are experiencing is the normal breaking in of the mattress or a mattress defect.
Phoenix