Here is more convenient reproduction of the issue for SMS in text mode. It is possible to observe the +CMGD command does not affect the status report storage
AT+CNMI=1,2,0,1,0
OK
at+cpms=“SR”
+CPMS: 13,30,1,2,0,75
OK
AT+CMGS=“+972525397371”
dd
+CMGS: 44
OK
+CDS: 6,44,“972525397371”,241,“24/01/17,13:46:12+08”,“24/01/17,13:46:32+08”,0
at+cpms=“SR”
+CPMS: 14,30,1,2,0,75
OK
at+cmgd=1,4
OK
at+cpms=“SR”
+CPMS: 14,30,1,2,0,75
OK