Why say for example:
в кухне нет радио and not
в кухне нет радиа?
Many loanwords don't decline in Russian, mostly those that don't intuitively fit into one of the existing paradigms (no regular Russian neuter noun ends in
-о preceded by a vowel), and to see why, it's helpful to turn to the social history of the Russian language.
Most early adopters of loanwords were people fluent in at least one foreign language, and thought of these words as essentially clippings from those other languages; in writing, it was—and still is—very common to include Western terms in their original Latin script. And so, essentially, those were islands of foreignness where Russian declension didn't apply.
That isn't the path taken by the vernacular—which tends to not only decline everything but also work around difficult and 'strange' foreign phonotactics; and thus, for example, the popularisation of the radio spawned the early vernacular form радиво, perfectly declinable—радива, etc.—but here, the social history of the language kicks in again. The spread of literacy in the Soviet times also lead to a lot of importance placed on language standards, which were regarded as ideology-neutral and thus inherited fairly intact from the Empire (save for the spelling reform, of course, but it was a one-off utilitarian thing).
And so it was that радиво and suchlike vernacular adaptations were levelled out, while declining 'indeclinables' in general continued to be regarded as a feature of 'rustic' and uneducated speech, with an even greater insistence on avoiding it than in pre-Soviet times, now that everyone could, and was expected to, aspire to the same general level of culture.
The words like
кофе etc are indeclinable.
The rules (in Russian): external link.