Polycarp encourages us to continue in our hope of righteousness.
"Let us then continually persevere in our hope, and the earnest of our righteousness, which is Jesus Christ, 'who bore our sins in His own body on the tree,' 'who did no sin, neither was guile found in His mouth,' but endured all things for us, that we might live in Him." (Polycarp 8)Some days we might not feel so righteous, and sometimes our righteousness seems so far away; we want to change but change seems to be taking much longer than we had hoped. In times like these we must persevere in hope, or as Paul put it, "do not grow weary of doing good." (2 Thessalonians 3:13) The reason for such overcoming hope is because our hope is not in ourselves; we are not trusting in our own strength, will, or desire. Our hope is not a reason but a person: Jesus Christ. We hope in righteousness because we trust in Jesus and we believe that He is "working in us that which is pleasing in His sight." (Hebrews 13:21)
This being the case, let us have patience.
"Let us then be imitators of His patience; and if we suffer for His name’s sake, let us glorify Him. For He has set us this example in Himself, and we have believed that such is the case." (Polycarp 8)
The suffering that was most pressing upon them was martyrdom and, while we might not face that on a daily basis, there are still other things that press down upon us; we all experience suffering in this life in our own way. Yet in all these things, because of our hope, we can have patience and still glorify God.