Seems that RecordPad could fit, althought not free. The most important feature: "Record only when you are speaking with voice activated recording".
See also the "Record Settings", from its detailed features page with screenshots: the program allows you to set a "maximum recording time", and choose what the program has to do once this limit is hit: stop or start recording a new file, which seems convenient for you.
The "Transmit" and "Output" settings may be of help for you too, since you can configure what to do automatically for each recording once is done (sending to FTP, mirror to a folder or execute an external tool -say for cleaning your oldest files?-, and also you automatically set a new file name pattern (sequence number and others, so you could always easily find your 'last' or even older records).
I think it's a pretty flexible solution if no other software matches exactly your desire. Claim to work on Windows 10, XP, Vista, 7, 8 and 8.1, and there are also versions for Mac, Android & iPhone.