I had a 1h05 connection 2 weeks ago. The flight left LHR 30 mins late.
When arriving in Dubai I legged it to the connecting gate where I arrived about 30 mins ahead (10 mins before gate closes) to find they had tried to offload and rebook me!!! After heated discussion this was reversed.
By bag didn't make it until about 6 hours later - they gave me $50 to buy a clean shirt.