You must study binary arithmetic. Sign flag is not enough to identify the result of the signed addition. There should be another flag called overflow which will identify if resulting value is correct or not.
8085 does not have overflow bit, unlike Z80's P/V bit, and you will not be able to identify correctness of the result using S flag only. It will be your task of programmer to ensure the overflow condition either by:
examining signs of input data. In your example, both are positive, but output is negative meaning there's an overflow. In general, values of differing signs will never trigger overflow; if signs of operands are the same, but result's sign is different, the result has overflown.
expanding size of the values to hold overflow bit. For this, in case of 8-bit registers, you may only have 6 significant bits, with two MSBs being sign  and overflow  respectively. If, after operation, these bits differ, it means overflow condition.
Your example extended to 9 bits
0.0.1000100 + 0.0.1000011 = 0.1.0000111
44h is positive 7-bit value, 43h is positive 7-bit value; result is having its sign and overflow bits set differently, 0 and 1, and it is overflow condition. Another example -
1.1.1100000 + 0.0.1110010 = 126.96.36.1990010 => 0.0.1010010
with carry discarded we see that sign and overflow bits are the same, thus result is correct, and in decimal it is -32 + 114 = 82.