Whenever I need to talk to her, she never answers her phone.
When I really need to speak with her, she doesn't pick up her phone.
この場合、次のように言うと自然な感じで良いと思います。
ーWhenever I need to talk to her, she never answers her phone.
「彼女と話す必要があるときにはいつも、彼女は電話に出ない」
Whenever I need to talk to her, .. で「彼女に用事があるときに限って」を表現できます。
to answer one's phone で「電話に出る」
ーWhen I really need to speak with her, she doesn't pick up her phone.
「彼女とすごく話す必要があるとき、彼女は電話に出ない」
When I really need to speak with her, ... でも「彼女に用事があるときに限って」を言えます。
to pick up one's phone で「電話に出る」
ご参考まで！
He can never be reached when I really need to reach him!
She doesn't pick up the phone when I really need to talk to her!
ご質問ありがとうございます。
① "He can never be reached when I really need to reach him!"＝「彼には絶対連絡が取れない、私が本当に彼と連絡を取りたいときに！」
② "She doesn't pick up the phone when I really need to talk to her!"＝「彼女は電話に出ない、私が彼女に本当に話さなければいけないときに！」
ご参考までに。
カナダ 
アメリカ合衆国 
