I you are creating a static path L2 extension in the EPG you do not have to define a subnet for the BD. And as you noted, the default gateway is the SVI for the vlan on your external layer 3 switch. Now, if you have devices in the same vlan in another EPG which is attached to the SAME BD then you need to define a subnet with a default gateway. the Default gw in the fabric is "different" from the external gw.
Since you are using the SAME ip address for the GW inside and outside is the reason why you are having intermittent loss.
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T.