There shouldn't be a conflict between the two NIC's like that. Also both IP address are from different range 192.168.51.x and 192.168.1.x so there shouldn't be a conflict either here.
The problem can be is that the metric value of one gateway is lower and that of the other is higher, so your internet traffic might be trying to go to the lower metric value gateway which is not used for net surfing and this is bcoz ur losing internet connection.
can be something like this.