The Arizona Territory secession/separation document you are quoting from was the second such document adopted by Arizona Territory. The first was adopted on February 3, 1861, also at Mesilla [present day southern New Mexico]. The February 3 document does not mention the interruption of the postal service as a reason for secession. It says in part:
Whereas, the continued aggressions and encroachments of the dominant party in the North, upon the equality and Constitutional rights of the South, have reached their climax in the election of a declared and open enemy of Southern rights, upon that one issue, and precipitated the Southern States into decided action; and the formation of a Southern Confederacy of States will probably follow; Therefore it is resolved --
1. That in the division of the Territories belonging to the United States, acquired by the blood and treasure of both North and South, Arizona naturally belongs to the South and should be attached to it.
3. That we repudiate a union or any connection with the Northern States under Black Republican principles, and that we cannot submit to being ruled by them as a Territory, without the loss of self-respect and the good opinion of the world.
7. That in case there is no formation of the Southern Confederation, that we desire to be annexed to the Republic of Texas, (in case Texas should secede and act independently,) as a part and parcel of that Republic, where we naturally belong. And that our delegates do all that they can to place us under the protection of the Lone Star Banner.
On March 16, 1861, after the Confederate States of America had been formed, the Arizona Territory held another convention in Mesilla and adopted the second secession document from which you quoted. They dropped their stated wish to be annexed to Texas and said the following instead:
RESOLVED, That we do not desire to be attached as a Territory to any State seceding separately from the Union, but to and under the protection of a Confederacy of the Southern States.
The mail service issue was not the only issue prompting the separation, but it was one of the reasons stated in the March 16 document. The parts you quoted from the March document are roughly the same reasons given in the February document. The mail service was mentioned as "another powerful reason" to separate in the March document [my bold below]:
RESOLVED, That the recent enactment of the Federal Congress, removing the mail service from the Atlantic to the Pacific States from the Southern to the Central or Northern route, is another powerful reason for us to ask the Southern Confederate States of America for a continuation of the postal service over the Butterfield or El Paso route, at the earliest period.
Thanks rustbucket. I think I’ll grab that one as well, or use that instead of the other text on AZ.