To me, back in service would be "um serviço operando novamente" (the service was restored) as in:
By then we expect most airports to be back in service. (o serviço de aeroporto - de voos estará funcionando novamente.)
Right now, there is no water in the immediate area, no power as well, no estimate when either one -- when water or power will be back into service. (o serviço de água e luz...)
from a site ===>>>Phones Back In ServiceNews and Events
by admin on June 24, 2014
Tuesday, June 24, 2014
Our phone service was restored about 10:30 AM. We appreciate your patience.
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Back on service (when a machine, say, a train a vessel (ship) etc go to repair/refurbishment and gets back, that is it was in a inactive state, sort of.) The service itself has not necessarily stopped, just a given machine.
SMRT Trains has also cited reasons of wear and tear of important components over the past two decades of service and water leaks from the air-conditioning system of some trains. ...On 5 November 2006, the first refurbished train, set 005/006, was put back on service.
The last trainset to be refurbished, set 075/076, had completed its refurbishment and put back on service on 2 January 2009.http://en.wikipedia.org/wiki/Kawasaki_H ... tries_C151
She was recommissioned in 1940 as the US Coast Guard Cutter WAGL-236 and sent to Norfolk. In 1943 her name was again changed, this time to the USCGC Hydrangea, because the USS Mayflower was back on service as a patrol craft. http://www.sail1620.org/Articles/mayflower-namesakes
There is also "back into service", when a cellphone, a telephone set, and others equipments are disconnected from a service and then are reconnected. For example, if you turn off a cellphone to recharge, or if it turned off because the battery had died then when you recharge it and your turn on, it comes back into service.
I didn´t cover all aspects of the question, just the ones I thought you would be more interested in.
For more, you can search the internet using the search engine of your liking.
Hope it helps.