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nlme: problem with fitting logistic function

Dear colegues 
I am trying to analyze growth data on mice. To do this I attempted to fit logistic curve using nlme package. However, the dataset I use is large (in total ca 20 000 measures on ca 3 000 individuals) with relatively complicated structure (several explanatory variables with interactions + random effect where individual offspring are nested within particular litters are nested within particular parental pairs). 
Although I had no problems to fit models, where the complexity of random effect was reduce (which is conceptually incorrect), the fitting procedure of the full model did not reach the 1 iteration after several hours. Do you have any idea how to solve this problem? 

Thank you very much for your advice 
Best regards 
Jakub Kreisinger