definite articles - Variations in the pronunciation of "the"

Although there are rather simple rules determining the pronunciation of "the", native speakers quite often deviate from these rules (including, e.g., TV shows). According to the Longman Pronunciation Dictionary,

The EFL learner is advised to use [ðə] before a consonant sound (the boy, the house), [ði] before a vowel sound (the egg, the hour). Native speakers, however, sometimes ignore this distribution, in particular by using [ðə] before a vowel (which is in turn usually reinforced by a preceding ʔ), or by using [ði:] in any environment, though especially before a hesitation pause. Furthermore, some speakers use stressed [ðə] as a strong form, rather than the usual [ði:].

My question is: when native speakers use [ðə] instead of [ði] before a vowel sound, do they do it on purpose or accidentally? If it is on purpose, how do they (typically) decide which pronunciation to use? What is a valid reason to use [ðə] before a vowel sound?

Answer

To summarize the discussion here and elsewhere:

In contrast to the pronunciation-based distinction between a and an, the pronunciation of "the" is not strictly determined by the pronunciation of the following word. The guidelines in, for example, the Longman Pronunciation Dictionary are in fact just guidelines for non-native speakers. If one listens closely to native speakers, it becomes obvious that [ðə] and [ði] are chosen relatively freely, irrespective of the following word. Hence, it is interesting that people who learn English as a foreign language are usually told by teachers and textbooks that the pronunciation of "the" follows the same strict rule as the distinction between a and an. This misconception can even be found on English language sites such as here.

A similar answer was given here.