Rye starter-- When is it okay to go into the fridge?

Toast

I've been maintaining a rye starter for the past week or so and at this point, the bubbles have gotten smaller (although they are definitely still forming). However, the starter initially was tripling and doubling in size within 12 hours... Now it's day 5 and the starter hardly doubles in size. After 12 hours, it's essentially at the same mark. Should I be concerned and feeding it more often than every 12 hours?

I had read that rye starters are very resilient and require less upkeep than say a white starter. Additionally, I'm going out of town for the next two days and I wanna stick the starter in the fridge, but I'm not sure when I should or if I should. How do I get the rye starter to rise again and when should I stick it in the fridge?

NKT,

 

I usually leave mine at room temperature for around 2 hours then it goes to my proofing fridge at 43F and I feed once per week,

 

Big Crusty