[susan53]

The first example isn't "random" - it would be incorrect with the article. When a singular countable noun is used with enough, there are two possibilities :

a) use enough of a : That would be enough of a reason to...
b) place enough after the noun without the article - as in your sentence.

Another example :
Lincoln was historian and economist ENOUGH to know that a substantial portion of this wealth had....

Obviously, if the noun is uncountable (relatively common) or plural (again rare), you don't need an article anyway, whether enough is placed before or after the noun :

...and had talent ENOUGH to fill the roles competently
(They) insist that there has not been time ENOUGH to institute reforms
He doesn't have sense ENOUGH to come out of the rain.
The disappearance of his will was proof ENOUGH of that
...with just about room ENOUGH for a properly performed hundred-and-eighty-degree turn
He simply didn't have funds ENOUGH to match your bet.

In all these cases enough could also be placed in front of the noun -eg, ..and had enough talent to fill the roles.... Placing it afterwards adds a little more emphasis.

The second example is, as it stands, incorrect and unlikely to be said. Much more likely is that the "a" was there, but so reduced phonetically that you didn't perceive it. I suspect this may be the case at other times when you wonder why the article was omitted too. Because English is a stress-timed language, many unstressed syllables are so reduced in quality that they are barely "there" at all and therefore difficult to perceive. This would certainly be the case with this sentence spoken fairly rapidly - you can hear me saying it if you click here : http://vocaroo.com/i/s1tIw0T31lRN Notice how both the first and second "a" almost disappear, as do the first and second "of". The second vowel of "medicine" (which is unstressed) disappears entirely.