How to avoid multipath noise
Moving your body close to the receiver will create this effect. Are you sure that this isn't happening? 

The bottom line with RSSI is, if one receiver has a much weaker signal than the other, the effects of local body movements will appear much more pronounced. RSSI is (usually, in a lot of RF chips) a logarithmic output proportional to dbV (or dBm) received on the antenna so a lower output level may have variations on it that can be much more easily seen than when RSSI is higher.

You may also be witnessing on the device with the "flat" RSSI saturation of the input transistors. This means RSSI is maxed out and will inevitably look flat.

Here's a picture of RSSI output voltage against received power: -



If your directly received signal is -90 dBm and you have a reflected signal at -91 dBm your net RSSI might vary between -88 dBm and -92 dBm whereas the same level of reflected signal adding or subtracting to a directly received signal of -80 dBm might produce a figure that varies between -79.99 dBm to 80.01 dBm - i.e. hardly any noticeable variation.

Notice also  that a strongly received signal (> -50 dBm) will tend to be on the more flattened part of the scale.