Learn Russian: Если бы не ваше вмешательство, мы бы потеряли клиента. - If it weren't for your intervention, we would have lost the client.

Exactly! Usually, showing absence requires the genitive case (like in у меня нет времени). However, the structure если бы не is a fixed idiom meaning 'if it weren't for.' The noun or pronoun that follows it must always take the nominative case.

Why is the particle бы used twice in this sentence?

In Russian counterfactual conditionals (situations that aren't real), you must use бы in both the 'if' clause and the 'then' clause. The first бы pairs with если to set up the hypothetical condition, and the second бы pairs with the past tense verb потеряли to show the hypothetical result.

Why does the direct object клиента end in -а?

It is in the accusative case because it is the direct object of the verb потеряли. For masculine animate nouns (people and animals, like клиент), the accusative form is identical to the genitive form, which is why it takes the -а ending here.

Is вмешательство related to the verb for 'to interfere'?

Yes, it is the noun form of вмешиваться or вмешаться, which mean to intervene or interfere. The neuter suffix -тельство is a common way to turn verbs into abstract nouns in Russian, much like '-tion' or '-ment' in English.