We have open PostFinance accounts in Switzerland and they updated our accounts with our address here in the UK - not a problem at all. However, we're both Swiss citizens, I'm not sure if that makes a difference or not.
I opened my PostFinance account as a tourist in 2008 with a US address, no problems. Obviously I am not a Swiss citizen, and in fact I never was a resident in Switzerland.
When I had a UBS account and a UK address I wasn't allowed to use e-banking from abroad other than to view, i.e no transactions. That was some years ago maybe the rules have changed - maybe ask.
I know UBS may cause some trouble for Americans returning home. Does swisspost care? I'd rather not move my money because Swisspost is actually a good bank!
When I left Switzerland and moved back to the UK one of the only things HMRC were really interested in was my account with Credit Suisse and if I planned on keeping it. Don't imagine this has changed much given the articles in the press over the last year or so.
Not all accounts are the same. You need to check out the rules on the account to find out if you can keep it open.
The normal account that banks give to residents for the purpose of receiving a salary, making rent payments etc... often have additional rules attached to them such as you must inform the bank if you are going switch your salary payments to another account or you are intending to leave the country. Usually in such cases they will close the account and may offer you another type.
I will soon be leaving Switzerland for Canada and checked with Credit Suisse about keeping open my bank account (in several currencies). No problem, I was assured, except that it will cost CHF 240 per year. (70CHF if moving to an EU country). There would be no charges if you have over CHF 250,000 in your accounts.
I moved in and out of CH several times, but never ever closed my account.
I asked the paperwork to be sent to friends or family address (just ask to be delivered C/O), and kept enough money on it to be charges-free...
It saved me the effort of setting it up again and again, gave me a long-term status with the bank, a safe haven to send money to whenever I needed; with no hassle.