British duo Heather Watson and Laura Robson suffered exits in the second round of the Aegon International.
Watson, 20, who is ranked 110 in the world, went down 7-6 (7-5) 6-1 to Czech seventh seed Lucie Safarova.
Robson, 18, who claimed a surprise win over
49th-ranked Maria Jose Martinez Sanchez on Tuesday
, was defeated 6-4 7-5 by Ekaterina Makarova of Russia.
is also out losing 6-2 3-6 6-3 to seventh seed Philipp Kohlschreiber.
Baker, who was the only remaining Briton in the singles draw by the time he went on court in Eastbourne, was broken twice as the German won the first set.
He came out strong in the second set and converted one of two break points to take the match into a decider.
Kohlschreiber, ranked 171 places higher than Baker, raced to a 4-0 lead in the third set, converting two break points to secure his place in the quarter-finals.
The German is joined in the last eight by American
who beat Jeremy Chardy 6-2 7-5 in just 84 minutes.
Roddick, who made it through
the first round after his opponent Sam Querrey
was forced to withdraw through injury, had seven break points in the opening set, eventually converting two.
The second set was a closer affair, although the seventh seed did have five more break points, which he failed to to take advantage of.
The three-time Wimbledon finalist will now face Italian Fabio Fognini on Thursday.
Reigning women's champion
of France eased to a 6-2 6-2 triumph over Canadian Aleksandra Wozniak.
beat Chanelle Scheepers 6-3 6-2, while Russia's
edged a closely-contested meeting with American Christina McHale 7-5 3-6 6-4.
In the other ladies matches both the eight and ninth seeds are out,
(8) beaten 6-4 3-6 6-1 by Tamira Paszek and
lost 6-1 1-6 6-2 to Klara Zakopalova.
There were mixed fortunes for the Britons in the doubles draw with
beating Pablo Andujar and Albert Ramos 6-3 6-0 but
were beaten 6-2 4-6 11-9 by Matthew Ebden and Donald Young.
In the last match on court at Eastbourne
, who are seeded 13th at Wimbledon, beat Israeli pair Jonathan Erlich and Andy Ram 7-2 (7-2) 7-6 (7-2).