OK, so we now know it is an issue with the base station. Lets again go thru some basics.

1) The MRF-350 has 2 parts. The base unit (MRF-350) and the antenna module (RFX-250). Both can be sold in the "i" version (MRF-350i & RFX-250i). Do both your antenna module and base station match - meaning are both "i" or both non-"i" versions.
Continuing the above, is your MX-990 an "i" version or non-"i" version?
All 3 pieces have to match in order for the RF to work. Just need to make sure either none of the pieces have an "i" at the end of the model number. Or all 3 do have the "i"

2) How are you connecting the MRF-350 and RFX-250 together? With the supplied mini-jack or a 3 conductor wire?

3) There is a power light on the MRF-350 and a power light on the RFX-250. Are both on solid.
There is an RF light on the RFX-250. Is that what's blinking you mentioned? There is also a Status light on the MRF-350 (indicates the same thing as the RF light on the FRX-250) - is it also blinking?