Count and non-count
First, let me address the question of attaching the plural suffix -s. It is true that if we can attach -s to pluralize, we have a noun; but it's not true that if we have a noun, we can attach -s to pluralize. Ignoring obvious exceptions like irregular plurals (children) and zero plurals (sheep), there's a major division of uses of nouns into count and non-count we need to think about.
What's a count noun? Basically, one you can count:
He has three briefcases. (count)
*He has three luggages. (non-count)
The noun luggage doesn't easily appear in the plural (luggages) with a cardinal numeral (three), so we conclude it's a non-count noun. To some extent, this is arbitrary, which we can tell because it differs according to language, and sometimes even changes over time in the same language (informations was once countable, but is no longer).
The same count / non-count distinction applies to nouns derived from the -ing form of verbs. And whether it's count or non-count does depend largely on how the speaker conceptualizes the word. There are a number of fairly broad categories, such as general concepts generally being uncountable and instances of activities being countable, but these are largely the same as for nouns derived in other fashions, and a complete account of the semantic categories that correspond to count and non-count is beyond the scope of this answer; the topic is treated in The Cambridge Grammar of the English Language (CGEL) starting on page 333, and further references can be found in its bibliography.
Running specifically is a count noun in a few uses (one of which I'll illustrate below), but is often a non-count noun indicating a general concept (as in Running is my favorite form of exercise). That means your intuition about runnings isn't enough to tell us whether it's a noun! In fact, it's a little bit more complicated than that, as we'll see below.
Testing for nounhood
So how do we tell if an -ing form is a noun, if checking for plural -s isn't enough? Basically, we want to see if the word is used syntactically like other nouns, and not like other verbs. To do that, we can use a number of tests (see CGEL, starting on page 81):
Does it inflect like a noun?
"While it's not fair to compare previous years, if you look back at recent runnings, the bubble horse had anywhere between 20 and 30 points, with non-restricted stakes serving as the important tiebreaker," Rogers said. (USA Today, 2012-06-14; Sports section, p.1)
By this test, runnings can indeed be a noun. But there are many other tests:
Does it take a determiner?
The walking wasn't so hard on my knees, but the running really hurt.
Does it take adjectives or adverbs as modifiers?
I solved the problem by quickly running to the store.
Here we have an adverb modifying running, the head of a gerund-participial clause.
Slow running is easier for me than fast running.
Here we have an adjective modifying the deverbal noun running, head of a noun phrase.
Does it take verb-like or noun-like complementation or modifiers?
The most famous running of the bulls is that of the eight-day festival of Sanfermines in honour of Saint Fermin in Pamplona [...]
Here we have not only a determiner (the), an adjectival phrase (most famous), but an of-phrase as well.
When you see a form like running, it may be verbal or deverbal. You have to look at the particular use to decide.
Semantic limitations on deriving nouns from -ing forms
There aren't really specific limitations on what sorts of verbs can undergo this derivation. Of course, they must have an -ing form, so defective verbs like must and beware are ruled out. And in many cases a corresponding noun already exists with a different shape, like classification in place of classifying. Even in those cases, using the -ing form as a noun is still usually possible, though as CGEL notes (p.1702):
In such cases the ·ing formation often tends to sound (in varying degrees) less idiomatic, less natural than the other, but not to the extent of being ungrammatical.
But in other cases, such as run and running, a deverbal noun exists with another shape, and we can see a clear difference in meaning:
I'm going out for a quick run.
??I'm going out for a quick running.
We might treat cases like these as an example of blocking, with the existence of the noun run preventing the use of running with the intended meaning.
Cases like this aside, this sort of derivation is really fairly productive in English. It is true that it's probably more likely when the original verb refers to an action or process, but that's not exactly a semantic limitation, more of a tendency. I don't believe deriving a noun from the -ing form of a verb has any special semantic requirements.
