I'm no expert, but in my understanding you can roll 401k funds that were rolled into an IRA only so long as the ira in question has never had any funds from any other source. However, my question is, why would you want to do this? You can do the backdoor roth from that traditional ira just fine. There is no advantage to rolling it all into another 401k, as far as I know.
Quidnon?, I think you may have a misunderstanding about what a backdoor is. You can convert a tIRA into a r.IRA and pay the income tax on the conversion, but this is not a backdoor roth. A backdoor roth is when you contribute to a non-deductible tIRA (non-deductible because you're over the income limit under which you can deduct tIRA contributions), then roll this into a r.IRA. This is possible because of a few peculiarities of how the laws around IRAs are written: 1) r.IRAs have an income limit over which you are not allowed to contribute, 2) t.IRAs have an income limit over which you cannot deduct the contribution, but no income limit prohibiting contributions (afterall, why would you contribute to a non-deductible t.IRA you'll have to pay taxes on later), and 3) you can convert a t.IRA to a r.IRA whether or not it was deductible. This is the backdoor roth (contribute to non-deductible t.IRA then convert to r.IRA)
The reason you would not want any existing t.IRA accounts from rollovers or previous deductible t.IRA contributions is that any t.IRA to r.IRA conversion is considered to come from all t.IRA's a person holds in proportion to the size of the accounts, so if you try to convert that non-deductible t.IRA in a backdoor roth conversion, but have existing rollover or deductible t.IRAs, then you will pay tax on the conversion at your marginal rate when you'd really rather keep that tax deferred money as tax deferred until you retire to a lower marginal tax rate.
Mother Fussbudget, having losses in your IRA shouldn't really be a factor. The issue you need to figure out is whether you 401k allows incoming rollovers from IRAs. Talking to HR and/or getting the plan documents so you can read through them would be the thing to do.