You mention this affects coming out of 'sleep' but the Intel CIR connectors are capable of powering on from S5 sleep state - exactly what sleep state are you talking about? Is there any chance there have been power cuts or mains power 'fluctuations'/brown outs etc on the occasions when it doesn't power up by the remote if it's S5 (wake from powered off state) you're talking about?
Do you have a UPS (uninterruptible power supply) that you could trial with this system just to rule out mains supply problems from being a contributing factor. Have you used known good (or even better brand new) batteries in the remote control to rule out a weak or intermittant signal from it as the cause? As for the USB mouse/keyboard issue, how are your USB Root Hubs set up in Device Manager - the common setting is a tick in the box to 'Allow the computer to turn off this device to save power' and no tick in the box underneath to 'Allow this device to wake the computer' - try swapping those around on the hub used for these devices to see if that makes a difference to this issue. Also check the power management tabs on your mouse and keyboard properties to ensure 'allow this device to wake the computer' is ticked.
This is coming out of S3. I haven't tried S5 extensivly, so I can't say if it experiences the same issue. Right now I'm doing preliminary testing and is all within a short time (a couple of hours), so there should be any power fluctuations. There is no UPS. For the battary in the remote, I'm using known good, rechargables.
The USB keyboard and mouse are connected directly to the PC, so I'm not sure why the OS would keep the ports off after S3.
Ordinary dry cells and alkalines produce 1.5 volts each but rechargables only produce 1.2 volts each so even though the batteries are charged, it'd still be worth trialling ordinary cells just to make sure your remotes tolerance to lower voltages isn't an issue.
Sometimes drivers don't behave exactly as they should with regards to hardware and power saving functionality so give these settings a try and report back. I'm assuming all the latest drivers installed for your motherboard include the chipset drivers and you're not just relying on the OS provided ones. Also use the latest keyboard and mouse combo drivers rather than using OS ones.