If the depreciation has been run for the month, can we still write down/off any assets in that period and re-run the depreciation. Or will we have to do in the next period.
Having depreciation processed for a fixed asset on the same month of the disposal will not stop you from writing it off (selling it).
Any depreciation that was processed for that asset on your current financial year will be automatically reversed. No other asset will have depreciation reversed when you do this, so there will be no need to re-run depreciation for everything again.
There is a setting under Admin / Settings / Fixed Assets / Manage Fixed Assets Types where you can set any type to allow depreciation during the year of sale. That means if you sell an asset that belongs to a type that has the setting ON, the depreciation of the year of sale will NOT be reversed. This is not a common setting to have turned on since in New Zealand the vast majority of assets cannot claim depreciation on the financial year when they were sold, this is an exception that only your accountant can advise if it is applicable for your business or not.