With typical commodity routers this is the case as has been pointed out. Perhaps the easy way to think of the situation is this;
The "repeater" router, having only one radio (i.e. tranceiver), can either transmit or it can receive at any instant. It can't do both because it's own transmitter would have such a high signal level in the receiver as to render the receiver useless.
So, it has to receive data half the time at the full bandwidth "B" and transmit it half the time at the full bandwidth "B". So, going through a wireless hop will reduce the overall data rate achieved to B/2. Anything other than half the time for each will either cause data loss or dead time.
Today, with dual-band devices readily available on the market, it's possible to use one band range (e.g. 5GHz) for one-to-one links and the other band range (e.g. 2.4GHz) for subsequent access point operation without loss of data rate as forced by a single transceiver.