Then too there may be the factor that, while powerful enough in herself at this point Alice is, she may mot be as powerful as she once was prior to The Blink.
For instance, what happened to her Warhammer did The Blink 'Depower' Alice and other Supersoldiers of her class?
Perhaps, but if the Blink diminished her powers then why not Church? Alice knew as soon as she saw him again that she and Sedna were no match for him, but if the Blink reduced their abilities then Church would be similarly affected.
And yet Church appears to be more powerful.
Or alternatively Alice, to defeat him, would have to unleash forces which would cause such a level of collateral damage that it would have unacceptable effects on those around that she is trying to protect.
That's a possibility too because even though the archaeophiles weren't under the same protection as her town she probably wanted to avoid unnecessary casualties, however, now that they are in space she could've struck Church in such a direction that he would fly far enough away from the habitat and certainly Earth for her to discard all restraint in fighting him. After that first punch she's on the defensive until he finally smashes her helmet which seems to confirm that she was never a match for him anywhere.
It's possible that since the Blink she no longer has access to technological assistance. Like the warhammer and rock-liquefying orbital strikes. So far we've only really seen evidence of incredible strength and toughness and the ability to summon armor around her. She did threaten Sedna with entombment, but she it may have been a bluff to calm her down. Without the immortal's external assistance, it could be that Church is the physically stronger. He's certainly much faster.
That seems to be the most likely explanation. Without external assistance and weaponry Alice never would've won that battle and knew it as soon as she saw Church.
The bulging eyes in the 5th panel received the most notice, but I'm concerned something else might have popped considering all the red droplets flying outward and pinkish hue on the bark Alice's head is being crushed against. She'll probably survive this, but I fear she might suffer some kind of brain damage. If the praeses finally intervene the timing couldn't be better. If Church is an unthinking brute then they may have countermeasures to subdue him. Alice would normally outsmart such methods, but if she's knocked out after this fight they won't have a problem capturing her too. Sedna with the help or Ardent and Gavia may be the only people that can ultimately thwart whatever they have planned.