I'm not sure that the pronunciation changed, it is probably more a matter of accent or colloquialism. There might actually be a "re-spite" meaning to spite again, but probably not. --> Respite "res-pit" is from the old French word "respit", which is from Latin "respectus" refuge, looking back.
In fact, the modern development in field of science and technology and especially in Information Technology has affected all areas of life and language as well. Due to its influence on our daily life we started to use the language which is more easy to speak and we speak it without caring the pronunciations. We just want to communicate message that's why not only many pronunciations have been changed but spellings of many words have also been altered. For example "colour" and "color". Similarly we tend to you abbreviations instead of complete word that is why some words are also mispronounced. And that's the reason.