Well you have answered the question for yourself - it's out of support - so you won't be getting that from Cisco.
You also haven't mentioned what version of software you're using at the moment and whether it's lightweight or autonomous. If it's lightweight then the software version is determined by the controller. If it's autonomous then you need to know what version you think it should have and then your only hope is to search for that and see what you can find.
As far as I know the last autonomous version was c1140-k9w7-tar.153-3.JD17.tar and for lightweight the last official WLC release was 8.3.150.0.
There's no guarantee that the 'bugs' you think you've found will be fixed in that release though - that technology is now very out of date and there've been a lot of fixes since then.
Could you advise how to convert an aironet C1140 to lightweight? how to find the last capwap image for that out-of-support APs? I just have this in flash c1140-k9w7-mx.124-21a.JA1, and I want to transfer it to lightweight? your support means a lot.
There are LOTS of guides and videos out there - search google for "cisco ap convert autonomous to lightweight"
You can use any k9w8 image to convert to lightweight - the AP will then download the correct version from the WLC when it joins. So search for any suitable file by name and see what you can find - for example you might find something like c1140-k9w8-tar.124-23c.JA2.tar which you can use.
