The accepted answer by @krysta may not be the full story: it depends on the way words are repeated.
I understand from @tsykora's question that words are repeated without a separation (syllables are produced at a fixed pace). Kounios et al. used spoken words (mean length of 544 milliseconds) that were repeated several times at a fixed interval of 800 milliseconds. This means that blanks (no sound) separated each presentation of a word.
The blank period between words is of importance since repeated words in a blank context may not "sound very weird" (words are clearly, physically, separable) but only loose their meaning. In a no-blank context (continuous speech), both meaning and percept change. An auditory example can be found in the "ILLUSORY CHANGES OF REPEATED WORDS: THE VERBAL TRANSFORMATION EFFECT" section (http://www4.uwm.edu/APL/demonstrations.html). For instance, while listening to repetitions of the word "rest", listeners are likely to switch between perceiving it as a repetition of "rest" and "tress" or "stress" (Warren & Gregory, 1958).
The verbal transformation effect originates in a multistable representation of a speech form. Pitt and Shoaf (2002) argues that one possible cause is the perceptual regrouping of the acoustic elements that make up a word. It involves some top-down processes in the perceptual organization of speech. A visual analogue of such illusion is found in the Necker cube where the percept changes according to where the eyes land (http://en.wikipedia.org/wiki/Necker_cube).
Such acoustic phenomenon makes me think of a statistical learning in language acquisition in children. It has been shown by Saffran and colleagues that a child can learn to segment a continuous speech into distinct words using transitional probabilities between syllables. In the context of repeated words, a word boundary is first placed between "ted-re" of "re-pea-ted-re-pea-ted" because "ted-re" is not frequent in English while the two other transitions are frequent. Going further in the auditory sequence, repetitive presentation of an utterance promotes alternative groupings of the acoustic elements because the elements occur at regular, predictable points in time (Bregman, 1990). Here, repeating a word at a fixed syllable pace abolishes the frequency of the syllable transitions (the frequencies are momentarily all equal) so that "pi-a-no-pi-a-no" is sometimes heard as "piano" and sometimes "anopi".
Bregman, 1990. Auditory scene analysis: The perceptual organization of sound.
Kounios et al., 2000. Memory & Cognition ; http://www.psychonomic.org/pubmed/mc/mc-28-1366.pdf
Pitt and Shoaf, 2002. JEP:HPP ; http://lpl.psy.ohio-state.edu/documents/PittShoafVTE-17_000.pdf
Warren & Gregory, 1958. An auditory analogue of the visual reversible ﬁgure, American Journal of Psychology.