Indian languages are syllable-timed. Native English is stress-timed. These terms refer to how the units of speech are divided up according to the flow of time, comparable to the way musical notes are scored according to measures and time signatures. These are two very different ways of allocating speech sound to time measurements.
Indian English is spoken syllable-timed, which is the main reason it’s difficult to understand for anyone not used to hearing this.
You are used to English spoken stress-timed, which like the poetry of Matthew Arnold can have any number of syllables in a given length of time, but only a certain number of stressed syllables. In spoken English, the unstressed syllables are de-emphasized and often slurred over. Our ears are used to catching the stressed syllables and constructing meaning out of those.
Indian English is so impenetrable to you because they don’t really have stressed syllables the way we do. The audible signposts to mark out the flow of speech that you’re trying to listen for just aren’t there. Instead, Indian English patterns the syllables in a constant flow. If any stress is incidentally given to a syllable (often not the one you expect to hear it on, as DeadlyAccurate observed), it is not significant for the Indian English speaker. That throws off the native English-speaking listener.
My suggestion is to consciously focus in on each syllable and train yourself to hear the actual speech sounds being pronounced, and to forget for the moment about trying to catch the stresses. This is more akin to getting meaning from reading text, in which each letter is equal and stresses are not transcribed in the writing (at least, they’re not usually transcribed in writing!).
A French professor told me once that casual French speech emphasises (like English) the pattern of stressed syllables, to the point where the talking-drum-like intonation conveys the meaning of familiar phrases, even when the phonemes themselves are slurred. He gave as the example somebody who gets onto a Parisian bus or taxicab and mumbles the name of a familiar place; the driver will know what the passenger is asking for just by the pattern of intonation, not by making out individual phonemes. The professor told us we will never sound like native French speakers unless we develop this intonation pattern.
So these Indian English speakers have no idea of the intonation pattern, even though that’s what you’re listening for. Instead, if you ignore intonation and stress, and listen for the individual phonemes and let your brain assemble them into words, that will convey the meaning to you.