I have the same problem. It seems to be around 2000-3000rpm. If you hit the accelerator all you get is engine noise with no torque! It is very dangerous, like you said it occurs just when you need the acceleration.
I do not believe it is the injectors. I think we need the engine controls to be re-programmed or flashed. I have a sport manual mode and have now learnt to quickly switch it to manual, get it into 2nd gear and accelerate out until it is fast enough to switch back into automatic mode.
I could be wrong but I think I still may be in 3rd gear instead of 2nd. This occurs when slowing down and then speed up out of a turn. The engine does not get enough torque but is in the wrong gear. I think it is a down shifting problem as it stays in the higher gear too long.
I spoken many times to the dealer and their answer is they do not see any fault codes. I know this is an issue also with the Mazda3 of which one of my friends owns and also reports the same problem. So far we are not getting any satisfaction in getting this fixed!
For now I will continue to operate in manual mode.

 

Remember that mine didn't give fault codes for a long time (from Aug to Dec) yet I had the poor performance.. Have them check the connection from the Oxygen sensor (O2) connections. Or if out of warranty. Buy some contact cleaner/lubricant) and open spray and close all connectors you can reach or get access to. I don't known exactly where the connector was because I wasn't shown, only told. Mine has been great since and the consumption is back to the 30MPG.

 

The fault light come back on the next day. I've been driving it ever since. They eventually put a new oxygen sensor in a week ago and again the light came back on. The Car has been left at the Mazda garage and we are using a Ford Focus until they cure the problem. I have been informed they think it's an injector or injector control problem and are waiting for replacement. When I ask them what's wrong or what are the fault codes they avoid telling and change subject. I did see the code when the RAC man came on the easter weekend. I see 134 and 113. Even though a mazda 5 was not on the data base only used mazda MPV and mazda 6 I thought I saw. They have had the mazda 5 for 1 week now. I was getting 19 MPG and the poor performance as previously mentioned.

 

I got my mazda 5 back on Friday (10 days later). I was told it has had a new PCU (powertrain control unit). Although there in no engine light on only for the first few miles did it feel better. The average (on the trip computer was 35mpg) But when I went out next time it felt weak again but getting 25mph, which is better than the 19mpg I got when I took it in.
UPDATE:- the MPG is getting better now at 29.6 and creeping up. It's as if engine or exhaust was sooted up and is eventually clearing and flowing better. But I'm sure this doesn't happen with modern electronically controlled engines. I'm happier now. Hopefully this is the end of it. After 1 year.