Попробовал с тем же mail.ru, всё работает. Может прошивку стоит обновить, у Вас сейчас какая?
Привожу лог:
RDY
+CFUN: 1
+CPIN: READY
Call Ready
SMS Ready
AT
OK
AT+GMR
Revision:1418B04SIM800C32_BT_EAT
OK
AT+SAPBR=3,1,"APN","internet.xxxxxxxxxx"
OK
AT+SAPBR=1,1
OK
AT+SAPBR=2,1
+SAPBR: 1,1,"xx.xxx.xxx.xx"
OK
AT+EMAILCID=1
OK
AT+EMAILTO=30
OK
AT+EMAILSSL=1
OK
AT+SMTPSRV="smtp.mail.ru",465
OK
AT+SMTPAUTH=1,"
[email protected]","password"
OK
AT+SMTPFROM="
[email protected]","username"
OK
AT+SMTPSUB="Hello"
OK
AT+SMTPRCPT=0,0,"
[email protected]","RCPTusername"
OK
AT+SMTPBODY=5
DOWNLOAD
OK
AT+SMTPSEND
OK
+SMTPSEND: 1
AT+SAPBR=0,1
OK
AT+CPOWD=1
NORMAL POWER DOWN