A friend of mine told me that the halacha of discouraging a convert three times has a little nuance - the convert has to make the second and third attempt (to persuade the rabbi to let him convert) at least six months after he got rejected the last time.
So, his implication was that if a convert gets rejected he can't approach the rabbi again the next day, or next week but has to wait for at least half a year before he asks the rabbi again to let him convert.
Does such halacha really exist? What's the source?
And if not, is there really any mandatory timeframe between each rejection i.e. how long does one have to wait before approaching the rabbi again?