Latin declension was simpler than that of Old Church Slavonic to begin with: OCS had 7 well defined cases, three numbers and 11 declension patterns (the so called o-stems, jo-stems etc) compared to Latin's 6 productive cases, two numbers and 5 declensions.
Cases were much more distinctive in OCS than in Latin where there was considerable syncretism.
Latin was introduced to populations who had a different native language, unlike the Slavic peoples.
A few sound changes rendered the Latin case system even harder to maintain, namely loss of final nasal consonants (or loss of nasal vowels) and loss of vowel length. So Latin rosa (Nom.), rosam (Acc.), rasae (Gen.), rosae (Dat.), rosā (Abl.) became rosa, rosa, rose, rose, rosa in Vulgar Latin, which means that there were only separate Nominative-Accusative and Genitive-Dative cases, just like in modern Romanian.
Most Slavic languages did not lose conjugations, they lost a few tenses because they became synonymous and eventually were replaced by another opposition: perfective vs imperfective aspect.