ObjectContext.ExecuteStoreCommand doesn't recognise parameter

The problem is that your code:

var parameters = new[]
{
     new SqlParameter("DesiredEndDate", SqlDbType.DateTime).Value = newUpperLimit,
     new SqlParameter("TasksToUpdate", SqlDbType.NVarChar).Value = idsToUpdate
};

is not creating an array of SqlParameters - it's actually create an array of the 2 Value properties. You can confirm this by changing your code to this (which will not compile):

var parameters = new SqlParameter[]
{
     new SqlParameter("DesiredEndDate", SqlDbType.DateTime).Value = newUpperLimit,
     new SqlParameter("TasksToUpdate", SqlDbType.NVarChar).Value = idsToUpdate
};

and this (which will compile)

var parameters = new SqlParameter[]
{
     new SqlParameter("DesiredEndDate", SqlDbType.DateTime),
     new SqlParameter("TasksToUpdate", SqlDbType.NVarChar)
};

parameters[0].Value = newUpperLimit;
parameters[1].Value = idsToUpdate;

You can also do this:

var param1 = new SqlParameter("DesiredEndDate", SqlDbType.DateTime);
param1.Value = newUpperLimit;
var param2 = new SqlParameter("TasksToUpdate", SqlDbType.NVarChar);
param2.Value = idsToUpdate;

ctx.ObjectContext.ExecuteStoreCommand("...", param1, param2);