At the moment, the business units which deal with REMO cases are going through a restructure. They have closed down the Greater London business unit and the one in Wales in the last 6 months. All cases for England and Wales are now being processed in Bury St. Edmunds and they are actively recruiting staff. So, at the moment, the application can take up to 3 months to be processed.
It is one problem of the REMO process that, after your application has been sent to the country where your ex is residing, you are left in the dark about what is happening with your application. According to a senior officer that I spoke to recently, it will probably take 6 months to get a reply.
Note that REMO is only a 'handling agent'. This means that they are not pro-active in your case, they are only there to check that your documents are legally compliant and to act as a conduit between your ex's country and the UK (you).
Also, remember that as your ex does not want to pay child maintenance, he is going to try as hard as possible to continue not to pay. I know that some states in the US put people in prison if they do not pay child maintenance.
As the other contributor mentioned, I would focus on creating extra income yourself.
I have succeeded in getting child maintenance from my ex, but it took years. 18,000 people have currently applied for this service and it does work, but very slowly and not for everyone, unfortunately. If your ex moves, you can put in another REMO application to the country where he resides, providing REMO has an agreement with that country