Off-ice, done at home, doesn't need to be a huge time commitment. 20 minutes a day, organized properly, is quite effective; alternating cardio (a mini-tramp is easy and gentle on joints) with own-weight strength training such as resistance bands, pushups, situps, etc. Look for a book called Conditioning for Figure Skaters: it's good, and there are nicely organized schedules and good understanding of the pre-pubescent skater.
My kids realized quickly that the "gains" made during the summer when they had time on their hands to do more off-ice AND on-ice were regularly lost when they stopped doing the off-ice portion when they returned to school, which was frustrating. Because the return to school coincides with the start of the competitive season ... well, the impact was noticeable. Thus, they/we make sure that efficient, effective off-ice training is done in the school period.
Interestingly, we had our first triple landed neatly and tidily after a change in footwear (better support), diet (more effective nutrition to support a growing body) and off-ice (change to core strength training) - occurred. It was far from coincidental. Sometimes small things have huge impact.