We are adopters of a little boy and in our situations delays have happened but we have just plodded on. The service is between the adoptive parent and the birth parent and so it isn't really (at least initially) directly for the child.
In that sense it shouldn't be capable of doing damage to the child, IMHO, it should just be a case of birth and adoptive parents corresponding.
I honestly don't think a three month delay is that bad. Our service has had delays due to staff going on leave or changing and these things are, sadly, quite hard to avoid.
To some extent I think it is the intention behind it, for birth and adoptive parents to try to correspond. There are so many things that could cause delays and frustrations. So just plodding on with it is, I think , the best option.
As adoptive parents we are sometimes responsible for the delays (speaking from personal experience). We've been dealing with a hugely stressful situation at the moment so would not want to be judged for those delays.
If it is early days for you, I'd just preserver, there are so many other things which could cause stress.
Hope things work out soon. 
River I hope your letter comes soon.