How to make an arduino wifi repeater?
An arduino wifi repeater would in theory be very slow. Since you need to record the bit stream to the internal memory, then switch the spi to the transmitter, and send the bit stream, im unsure about what would happen if you miss a few bits in the process. 

Arduino Wifi Shield - the price of a wifi shield 85 usd

Wifi repeater ebay the price of a wifi repeater 22 usd.

This makes me question why one would go through the troubble of making a wifi repeater of an arduino.

Even investing in a raspberry pi and a wifi dongle would be less expensive.