In part, yes, I could use a larger battery bank. It is currently 8 T-105 "golf cart" batteries, which gives 48V x 205AH = 9840Wh if they are completely discharged. Best to keep a lead-acid battery above 50% discharged, so that's just shy of 5kWh. For daily use I don't like to go more than 25% discharged, so 2.5kWh/day. When these are ready to be replaced, I plan to go with L16s which will double my capacity.
But I can only replace that and run the loads simultaneously during the summer. In winter, I'm doing good to get 3kWh/day from the panels. If the loads are left on the inverter during that time I won't get the battery bank fully charged. Summertime no problem, 6kWh easy - long as it isn't a cloudy day.
My fridge uses 1.6kWh/day, so it alone would almost fully consume my available solar power in winter. The LAN and servers "idle" (when my desktop isn't on) at a total of 120W or so, just shy of 3kWh/day. In summer it is my 24x7 load for the solar system, but again in winter I can't count on achieving that each day. Of course, the desktop only adds to that total number, making it worse.
I have written a program to monitor power usage and switch the loads to grid when the battery bank drops to 25% discharged, then back to inverter at 20%. Works well enough, but it means I discharge the battery in the evenings and it sits partially charged overnight. I need to add to that so it senses when the sun is up, and also "anticipates" sunrise by switching over to inverter in the wee hours of the morning - then the battery bank doesn't spend much time in a discharged state before recharge begins.
Or just spend more money on more panels and battery...!