Hi,
It's not exactly 4.38V , it may be in the range of 4.3V ... 4.45V in room temperature.
If VCC is above threshold it takes nom. 240ms for the output to get activated.
If VCC falls below threshold for nom. 20us it deactivates the output.
This maybe is the case when your switcher starts. When activated it draws current,
the voltage at the input capacitors drop..maybe below the threshold.
I wonder why you hide the type of your switcher. It is involved in overall /RESET function. Thus usually we need to verify it.
Since the MAX809 output is at least OFF for 240ms while only ON for 20us (in worst case) a DVM can not detect this.
You need a scope to verify what's really happening. If you don't have one, lend one or buy one.
For a quick DVM measurement:
What's the battery voltage at disconnected battery?
What's VCC voltage when you expect MAX809 output to be ON, but is OFF?
What's VCC voltage when the switcher works properly?
Klaus