You seem to be confusing morae and syllables. Syllables are units that have a nucleus which is typically either a vowel (which may be both a monophthong or a diphthong) or a sonorant, such as /l/, /m/, /n/ or /r/. The English words "ski" [ski:] and "sick" [sɪk] have just one syllable, while the word button [bʌ·tn] has two, with "n" being the nucleus of the second syllable.
It's important to note that syllables may vary greatly in length, depending on how many consonant they have, whether they are stressed, whether they have a diphthong or a monophthong and whether they have a long, short or elided vowel. The second syllable in "button" ([tn]), for instance, is very short since it is unstressed and it doesn't have any vowel at all, but rather the sonorant "n" that isn't really pronounced for a long time in English (in other languages it may behave differently). Syllables with diphthongs or long vowels, on the other hand are quite longer (this difference is more pronounced in some English accents than in other).
Morae, on the other hand, are quite different from syllable. These are rhythmical units of (relatively) fixed length, and they only count time - not the existence or absence of a nucleus and not even the existence of sound (the Japanese small tsu, っ, may count as a mora even in the cases where it ends up being just a silent pause). You can imagine a mora as the beat of an inaudible metronome that goes inside the speaker's head and represents the tempo of his or her speech: when you speak very fast, a single mora may take as little as a tenth of a second, and when you dictate something in an exaggerated manner it can take as much as two seconds.
Since mora is entirely a unit of length and not a standard structure for how phonemes may be joined together, you can see that long vowels and geminated (doubled) consonants take two morae, and the consonant 'n', when it comes without a vowel, takes a whole mora for itself. This means that even when there's a muted vowel (such as the /i/ in 士気), the consonant still takes an entire mora on its own. I believe that if you'd count the length of the audio samples on WWWJDIC you'll notice that they actually have roughly the same length (despite some of them having a muted vowel and some of them not).
What confused you, of course, was interpreting the Japanese examples as the English syllables you've heard and trying to count morae according that. But just as the concept of mora is not really useful for understanding when applied to English (at least when it is not sung or solemnly recited), the concept of syllable is quite alien to Japanese. You can divide Japanese to syllables if you want, but then you'd be dividing it by English (or German or Chinese or whatever) standards. Japanese phonology per se (and I'm not talking about unprovable universal phonology models here) has no internal concept of a syllable. Only the morae count.